Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The value of the definite Integral $text . end text stretchy integral subscript negative 2008 end subscript superscript 2008 end superscript fraction numerator f to the power of ´ end exponent left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis negative x right parenthesis over denominator left parenthesis 2008 right parenthesis to the power of x end exponent plus 1 end fraction d x text equals end text$

$f (2008) + f (- 2008)$
$f (2008) - f (- 2008)$
0
$f (- 2008) - f (2008)$

The correct answer is: $f left parenthesis 2008 right parenthesis minus f left parenthesis negative 2008 right parenthesis$

Related Questions to study

The integral $integral s i n invisible function application 2 x open parentheses 1 minus fraction numerator 3 over denominator 2 end fraction c o s invisible function application x close parentheses e to the power of s i n to the power of 2 end exponent invisible function application x plus c o s to the power of 3 end exponent invisible function application x end exponent d x text end text$ is equal to

The integral $integral s i n invisible function application 2 x open parentheses 1 minus fraction numerator 3 over denominator 2 end fraction c o s invisible function application x close parentheses e to the power of s i n to the power of 2 end exponent invisible function application x plus c o s to the power of 3 end exponent invisible function application x end exponent d x text end text$ is equal to

A point P moves in xy – plane in such a way that $left square bracket vertical line x vertical line right square bracket plus left square bracket vertical line y vertical line right square bracket equals 1 comma text where end text left square bracket. right square bracket$ denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to

A point P moves in xy – plane in such a way that $left square bracket vertical line x vertical line right square bracket plus left square bracket vertical line y vertical line right square bracket equals 1 comma text where end text left square bracket. right square bracket$ denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to

The value of $stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text$

The value of $stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text$

parallel

If function f(x) $equals c o s invisible function application x minus stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis x minus 1 right parenthesis f left parenthesis t right parenthesis d t comma text then end text f to the power of ´ ´ end exponent left parenthesis x right parenthesis plus f left parenthesis x right parenthesis text end text$ is equal to

If function f(x) $equals c o s invisible function application x minus stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis x minus 1 right parenthesis f left parenthesis t right parenthesis d t comma text then end text f to the power of ´ ´ end exponent left parenthesis x right parenthesis plus f left parenthesis x right parenthesis text end text$ is equal to

If $I equals stretchy integral subscript 0 end subscript superscript 12 end superscript fraction numerator d x over denominator square root of 1 minus x to the power of 2 n end exponent end root end fraction comma n element of N comma text end text$ then

If $I equals stretchy integral subscript 0 end subscript superscript 12 end superscript fraction numerator d x over denominator square root of 1 minus x to the power of 2 n end exponent end root end fraction comma n element of N comma text end text$ then

Statement - I : $ϕ left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis 3 s i n invisible function application t plus 4 c o s invisible function application t right parenthesis d t comma open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets ϕ left parenthesis x right parenthesis text end text$ attain its maximum value $text at end text x equals fraction numerator pi over denominator 3 end fraction$
Statement - 2: $ϕ left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis 3 s i n invisible function application t plus 4 c o s invisible function application t right parenthesis d t comma ϕ left parenthesis x right parenthesis text end text$ increasing function in $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text$

Statement - I : $ϕ left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis 3 s i n invisible function application t plus 4 c o s invisible function application t right parenthesis d t comma open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets ϕ left parenthesis x right parenthesis text end text$ attain its maximum value $text at end text x equals fraction numerator pi over denominator 3 end fraction$
Statement - 2: $ϕ left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis 3 s i n invisible function application t plus 4 c o s invisible function application t right parenthesis d t comma ϕ left parenthesis x right parenthesis text end text$ increasing function in $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text$

parallel

$f left parenthesis x right parenthesis equals open square brackets fraction numerator left parenthesis x minus 2 right parenthesis to the power of 3 end exponent over denominator a end fraction close square brackets s i n invisible function application left parenthesis x minus 2 right parenthesis plus a c o s invisible function application left parenthesis x minus 2 right parenthesis comma open square brackets times close square brackets$ denotes the greatest integer function, is continuous and differentiable in (4, 6) then.

$f left parenthesis x right parenthesis equals open square brackets fraction numerator left parenthesis x minus 2 right parenthesis to the power of 3 end exponent over denominator a end fraction close square brackets s i n invisible function application left parenthesis x minus 2 right parenthesis plus a c o s invisible function application left parenthesis x minus 2 right parenthesis comma open square brackets times close square brackets$ denotes the greatest integer function, is continuous and differentiable in (4, 6) then.

$text If end text f left parenthesis x right parenthesis equals open curly brackets table row cell s i n invisible function application open parentheses fraction numerator pi over denominator 2 end fraction left parenthesis x minus left square bracket x right square bracket right parenthesis close parentheses comma blank x less than 5 end cell row cell 5 left parenthesis b minus 1 right parenthesis comma blank x equals 5 text end text text i end text text s end text text end text text c end text text o end text text n end text text t end text text i end text text n end text text u end text text o end text text u end text text s end text text end text text a end text text t end text text end text x equals 5 comma left parenthesis a comma b element of R right parenthesis text end text text t end text text h end text text e end text text n end text text end text left parenthesis left square bracket. right square bracket end cell row cell a b to the power of 2 end exponent fraction numerator open vertical bar x to the power of 2 end exponent minus 11 x plus 24 close vertical bar over denominator x minus 3 end fraction comma blank x greater than 5 end cell end table close$ denotes greatest integer function)

$text If end text f left parenthesis x right parenthesis equals open curly brackets table row cell s i n invisible function application open parentheses fraction numerator pi over denominator 2 end fraction left parenthesis x minus left square bracket x right square bracket right parenthesis close parentheses comma blank x less than 5 end cell row cell 5 left parenthesis b minus 1 right parenthesis comma blank x equals 5 text end text text i end text text s end text text end text text c end text text o end text text n end text text t end text text i end text text n end text text u end text text o end text text u end text text s end text text end text text a end text text t end text text end text x equals 5 comma left parenthesis a comma b element of R right parenthesis text end text text t end text text h end text text e end text text n end text text end text left parenthesis left square bracket. right square bracket end cell row cell a b to the power of 2 end exponent fraction numerator open vertical bar x to the power of 2 end exponent minus 11 x plus 24 close vertical bar over denominator x minus 3 end fraction comma blank x greater than 5 end cell end table close$ denotes greatest integer function)

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text$

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text$

parallel

A function f from integers to integers is defined as $f left parenthesis x right parenthesis equals open curly brackets table row cell n plus 3 blank n element of o d d end cell row cell n divided by 2 blank n element of text end text text e end text text v end text text e end text text n end text text end text end cell end table text suppose end text k element of text odd end text close text and end text$ $f left parenthesis f left parenthesis f left parenthesis k right parenthesis right parenthesis right parenthesis equals 27 text end text$ then the sum of digits k is

A function f from integers to integers is defined as $f left parenthesis x right parenthesis equals open curly brackets table row cell n plus 3 blank n element of o d d end cell row cell n divided by 2 blank n element of text end text text e end text text v end text text e end text text n end text text end text end cell end table text suppose end text k element of text odd end text close text and end text$ $f left parenthesis f left parenthesis f left parenthesis k right parenthesis right parenthesis right parenthesis equals 27 text end text$ then the sum of digits k is

Let f(x) $equals left square bracket n plus p s i n invisible function application x right square bracket cross times stack I with hat on top left parenthesis 0 comma p right parenthesis comma n stack I with hat on top Z to the power of ´ end exponent p to the power of ´ end exponent$ a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )

Let f(x) $equals left square bracket n plus p s i n invisible function application x right square bracket cross times stack I with hat on top left parenthesis 0 comma p right parenthesis comma n stack I with hat on top Z to the power of ´ end exponent p to the power of ´ end exponent$ a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text end text$ is equal

If graph of the function y= f(x) is continuous and passes through point (3, 1) then $stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text end text$ is equal

parallel

Let f be twice differentiable real valued function satisfying $f to the power of ´ end exponent left parenthesis x right parenthesis not equal to 0 comma f left parenthesis x right parenthesis plus f to the power of ´ ´ end exponent left parenthesis x right parenthesis equals negative x g left parenthesis x right parenthesis f to the power of ´ end exponent left parenthesis x right parenthesis$ where $g left parenthesis x right parenthesis greater than 0 for all x greater than 0 text .If end text f left parenthesis 0 right parenthesis equals negative 3 text end text$ and $f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 4 text end text$ then
Statement -1: $vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0$
Statement -2: $left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus open parentheses f to the power of ´ end exponent left parenthesis x right parenthesis close parentheses to the power of 2 end exponent$ is decreasing $for all x greater than 0.$

Let f be twice differentiable real valued function satisfying $f to the power of ´ end exponent left parenthesis x right parenthesis not equal to 0 comma f left parenthesis x right parenthesis plus f to the power of ´ ´ end exponent left parenthesis x right parenthesis equals negative x g left parenthesis x right parenthesis f to the power of ´ end exponent left parenthesis x right parenthesis$ where $g left parenthesis x right parenthesis greater than 0 for all x greater than 0 text .If end text f left parenthesis 0 right parenthesis equals negative 3 text end text$ and $f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 4 text end text$ then
Statement -1: $vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0$
Statement -2: $left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus open parentheses f to the power of ´ end exponent left parenthesis x right parenthesis close parentheses to the power of 2 end exponent$ is decreasing $for all x greater than 0.$

Let $I equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator sin invisible function application x over denominator square root of x end fraction d x text and end text J equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator cos invisible function application x over denominator square root of x end fraction d x text . end text$ Then which one of the following is true ?

Let $I equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator sin invisible function application x over denominator square root of x end fraction d x text and end text J equals stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator cos invisible function application x over denominator square root of x end fraction d x text . end text$ Then which one of the following is true ?

$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

$text Iff end text text . end text minus y minus e to the power of y end exponent comma g comma negative y minus y comma y greater than 0 text end text$ andE.. $t minus stretchy integral subscript 0 end subscript superscript t end superscript f left parenthesis t minus y right parenthesis g left parenthesis y right parenthesis d y text , end text$ then-

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.