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

4ln

3

2

B1

2ln

3

2

C ln3

2

D1

6ln

3

2

Q. limn→∞

n + 1

n2 + 12+

n + 2

n2 + 22+. . . . . +

1

nis equal to

A π

4+

1

2log 2

Bπ

4−

1

2log 2

Cπ

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

1x4

2

dx equals -

(A) (B)

(C) (D) None of these

22

1log

1x2x

1x2x2

2

+ C 22

1log

1x2x

1x2x2

2

+ C

2

1tan–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