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

Let $text end text f colon R to the power of plus end exponent rightwards arrow R$ be a differentiable function with $f left parenthesis A right parenthesis equals 3$ and satisfying $stretchy integral subscript 1 end subscript superscript x y end superscript f left parenthesis t right parenthesis d t equals y stretchy integral subscript 1 end subscript superscript x end superscript f left parenthesis t right parenthesis d t plus x stretchy integral subscript 1 end subscript superscript y end superscript f left parenthesis t right parenthesis d t for all x comma y element of R to the power of plus end exponent comma text then end text f left parenthesis x right parenthesis equals$

3 lnx
lnx + 3
3 + 3 lnx
None of these

The correct answer is: 3 + 3 lnx

Related Questions to study

Area bounded by the curve $y to the power of 2 end exponent equals x plus 4$ and the line x+2y=4 is _____ sq. units

Area bounded by the curve $y to the power of 2 end exponent equals x plus 4$ and the line x+2y=4 is _____ sq. units

Area of the figure contained between the parabola $x to the power of 2 end exponent equals 4 y$ and the curve $y equals fraction numerator 8 over denominator x to the power of 2 end exponent plus 4 end fraction text is end text 2 pi minus K$ then K=

Area of the figure contained between the parabola $x to the power of 2 end exponent equals 4 y$ and the curve $y equals fraction numerator 8 over denominator x to the power of 2 end exponent plus 4 end fraction text is end text 2 pi minus K$ then K=

The area bounded by mini $left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 2 text end text$ and $m a x left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 4 text is : end text$

The area bounded by mini $left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 2 text end text$ and $m a x left parenthesis vertical line x vertical line comma vertical line y vertical line right parenthesis equals 4 text is : end text$

parallel

$f left parenthesis x right parenthesis equals stretchy integral subscript 1 end subscript superscript x end superscript fraction numerator tan to the power of negative 1 end exponent invisible function application t over denominator t end fraction d t semicolon x greater than 0$ then the value of $f open parentheses e to the power of 2 end exponent close parentheses minus f open parentheses fraction numerator 1 over denominator e to the power of 2 end exponent end fraction close parentheses text is end text$

$f left parenthesis x right parenthesis equals stretchy integral subscript 1 end subscript superscript x end superscript fraction numerator tan to the power of negative 1 end exponent invisible function application t over denominator t end fraction d t semicolon x greater than 0$ then the value of $f open parentheses e to the power of 2 end exponent close parentheses minus f open parentheses fraction numerator 1 over denominator e to the power of 2 end exponent end fraction close parentheses text is end text$

$integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals f left parenthesis x right parenthesis plus c text thenf end text left parenthesis x right parenthesis equals$

$integral left parenthesis square root of c o t invisible function application x end root plus square root of t a n invisible function application x end root right parenthesis d x equals f left parenthesis x right parenthesis plus c text thenf end text left parenthesis x right parenthesis equals$

If $text end text g left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis vertical line s i n invisible function application t vertical line plus vertical line c o s invisible function application t vertical line right parenthesis d t text then end text g open parentheses x plus fraction numerator n pi over denominator 2 end fraction close parentheses$ is equal to where $n element of N$

If $text end text g left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript left parenthesis vertical line s i n invisible function application t vertical line plus vertical line c o s invisible function application t vertical line right parenthesis d t text then end text g open parentheses x plus fraction numerator n pi over denominator 2 end fraction close parentheses$ is equal to where $n element of N$

parallel

If the primitive of $text end text s i n to the power of negative 3 divided by 2 end exponent invisible function application x s i n to the power of negative 1 divided by 2 end exponent invisible function application left parenthesis x plus theta right parenthesis text end text text is end text text end text minus 2 c o s e c invisible function application theta square root of f left parenthesis x right parenthesis end root plus C text end text$ then

If the primitive of $text end text s i n to the power of negative 3 divided by 2 end exponent invisible function application x s i n to the power of negative 1 divided by 2 end exponent invisible function application left parenthesis x plus theta right parenthesis text end text text is end text text end text minus 2 c o s e c invisible function application theta square root of f left parenthesis x right parenthesis end root plus C text end text$ then

$integral fraction numerator square root of s i n to the power of 3 end exponent invisible function application 2 x end root over denominator sin to the power of 5 end exponent invisible function application x end fraction d x text is end text$

$integral fraction numerator square root of s i n to the power of 3 end exponent invisible function application 2 x end root over denominator sin to the power of 5 end exponent invisible function application x end fraction d x text is end text$

Assertion : Two similar trains are moving along the equatorial line with the same speed but in opposite direction. They will exert equal pressure on the rails.
Reason : In uniform circular motion of magnitude of acceleration remains constant but the direction continuously changed.

Assertion : Two similar trains are moving along the equatorial line with the same speed but in opposite direction. They will exert equal pressure on the rails.
Reason : In uniform circular motion of magnitude of acceleration remains constant but the direction continuously changed.

Physics-General

parallel

Assertion : As the frictional force increases, the safe velocity limit for taking a turn on an unbanked road also increases.
Reason : Banking of roads will increase the value of limiting velocity.

Assertion : As the frictional force increases, the safe velocity limit for taking a turn on an unbanked road also increases.
Reason : Banking of roads will increase the value of limiting velocity.

Physics-General

A ball is rolled off the edge of horizontal table at a speed of 4m/sec. It hits the ground after 0.4 second. Which statement given below is true :

A ball is rolled off the edge of horizontal table at a speed of 4m/sec. It hits the ground after 0.4 second. Which statement given below is true :

Physics-General

A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/p revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is :

A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/p revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is :

physics-General

parallel

A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true :

A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true :

Physics-General

A point mass m is suspended from a light thread of length l, fixed at O, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are :

A point mass m is suspended from a light thread of length l, fixed at O, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are :

physics-General

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first :

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first :

physics-General

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.