Maths-
General
Easy

Question

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

  1. g left parenthesis x right parenthesis plus g left parenthesis pi right parenthesis    
  2. g left parenthesis x right parenthesis plus 2 n    
  3. g left parenthesis x right parenthesis plus g open parentheses fraction numerator pi over denominator 2 end fraction close parentheses    
  4. g left parenthesis x right parenthesis    

The correct answer is: g left parenthesis x right parenthesis plus 2 n


    g left parenthesis x plus n pi divided by 2 right parenthesis equals stretchy integral subscript 0 end subscript superscript x plus n pi divided by 2 end superscript   open parentheses vertical line s i n invisible function application t vertical line plus vertical line c o s invisible function application t vertical line d t 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 t invisible function application t vertical line right parenthesis d t plus stretchy integral subscript x end subscript superscript x plus n pi divided by 2 end superscript   left parenthesis right parenthesis d t close
    equals g left parenthesis x right parenthesis plus stretchy integral subscript 0 end subscript superscript infinity divided by 2 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 equals g left parenthesis x right parenthesis plus n stretchy integral subscript 0 end subscript superscript pi divided by 2 end superscript   left parenthesis vertical line s i n invisible function application x vertical line plus vertical line c o s invisible function application t vertical line right parenthesis d t equals g left parenthesis x right parenthesis plus n left parenthesis 1 plus 1 right parenthesis equals g left parenthesis x right parenthesis plus 2 n

    Related Questions to study

    General
    Maths-

    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 textthen

    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 textthen

    Maths-General
    General
    Maths-

    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

    Maths-General
    General
    Physics-

    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
    General
    Physics-

    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
    General
    Physics-

    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
    General
    physics-

    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
    General
    Physics-

    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
    General
    physics-

    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
    General
    physics-

    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
    General
    Physics-

    A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following :

    A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following :

    Physics-General
    General
    Physics-

    Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speed are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is :

    Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speed are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is :

    Physics-General
    General
    Physics-

    A ball is projected with kinetic energy E at an angle of 45degree to the horizontal. At the highest point during its flight, its kinetic energy will be :

    A ball is projected with kinetic energy E at an angle of 45degree to the horizontal. At the highest point during its flight, its kinetic energy will be :

    Physics-General
    parallel
    General
    Maths-

    A fair die is tossed three times. Given that the sum of the first two tosses equals the third. The probability that at least one ‘2’ has turned up, is equal to

    A fair die is tossed three times. Given that the sum of the first two tosses equals the third. The probability that at least one ‘2’ has turned up, is equal to

    Maths-General
    General
    maths-

    On a wall , a traiangle is drawn as shown in figure suppose you have thrown an arrow on the target triangle and it sticks at the interior of the triangle. If it sticks at a point P (x,y) with x<y, then you will win the game. The probability that you win the game ?

    On a wall , a traiangle is drawn as shown in figure suppose you have thrown an arrow on the target triangle and it sticks at the interior of the triangle. If it sticks at a point P (x,y) with x<y, then you will win the game. The probability that you win the game ?

    maths-General
    General
    Maths-

    An integer from the set of first 100 natural numbers is selected at random .The probability that the number satisfying the inequality n plus 1 subscript C subscript n minus 2 end subscript end subscript minus n plus 1 subscript C subscript n minus 1 end subscript end subscript less or equal than 100 is

    An integer from the set of first 100 natural numbers is selected at random .The probability that the number satisfying the inequality n plus 1 subscript C subscript n minus 2 end subscript end subscript minus n plus 1 subscript C subscript n minus 1 end subscript end subscript less or equal than 100 is

    Maths-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.