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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