Problems Solving on Integral Calculus · PDF file 28.05.2020  · Problems Solving...

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Transcript of Problems Solving on Integral Calculus · PDF file 28.05.2020  · Problems Solving...

  • Problems Solving on Integral Calculus

    By Ankush Garg(B. Tech, IIT Jodhpur)

    MATHEMATICS

  • Q. The value of xsinx2

    sin x2 + sin(ln6 − x2  dx is

    ln3

    ln2

    A 1

    4 ln

    3

    2

    B 1

    2 ln

    3

    2

    C ln 3

    2

    D 1

    6 ln

    3

    2

  • Q. lim n→∞

    n + 1

    n2 + 12 +

    n + 2

    n2 + 22 +. . . . . +

    1

    n is equal to

    A π

    4 +

    1

    2 log 2

    B π

    4 −

    1

    2 log 2

    C π

    4 − 2log

    1

    2

    D None of these

  • Q. Let f x = dt

    1 + t4

    x

    2

    and g be the inverse of f. Then the value of g′ 0 is

    A 1

    B 17

    C 17

    D None of these

  • The value of  

    1x

    1x 4

    2

    dx equals -

    (A) (B)

    (C) (D) None of these

    22

    1 log

     

     

    

    

    1x2x

    1x2x 2

    2

    + C 22

    1 log

     

     

    

    

    1x2x

    1x2x 2

    2

    + C

    2

    1 tan–1

    x2

    1x2  + C

  • Q. The area bounded in the first quadrant by the nornal at 1, 2 on the

    the curve y2 = 4x, x-axis & the curve is given by.

    (A 10

    3

    (B 7

    3

    (C 4

    3

    (D 9

    2

  • Q. The area of the region s enclosed by the curves y = x2 and y = | x | is

    (A 1

    3

    (B 2

    3

    (C 1

    6

    D 1