• date post

18-Oct-2020
• Category

## Documents

• view

8

2

Embed Size (px)

### 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