Integral Calculus Answers

Integrate with respect to x :
4x2.dx

Evaluate
∫
dx ) 1- x(
2
(a) x
5
/5 – 2/3 x
3
+ x + k
(b)
kx
3
x
3
+−
(c) 2x
(d) none of these
5.
∫
+
) x 1 ( ) 3x –1 (
dx is equal to
(a) x – x
2
– x
3
(b) x
3
– x
2
+ x (c) x – x
2
– x
3
+ k (d) none of these
6.
[
]
∫
x/1–x
dx is equal to
(a)
3
2
x
3/2
– 2 x
½
+k (b)
kx2x
3
2
+−
(c)
k
xx2
1
x2
1
++
(d) none of these
7. The integral of px
3
+ qx
2
+ rk + w/x is equal to
(a) px
2
+ qx + r + k
(b) px
3
/3 + qx
2
/2 + rx
(c) 3px + 2q – w/x
2
(d) none of these
8. Use method of substitution to integrate the function f(x) = ( 4x + 5 )
6
and the answer is
(a) 1/28 ( 4x + 5 )
7
+ k (b) ( 4x + 5 )
7
/7 + k (c) ( 4x + 5 )
7

9. Use method of substitution to evaluate
∫
+
52
)4x(x
dx and the answer is



10. Integrate ( x + a )
n
and the result will be

integral of( log x) power 2

integral of log x value is

Q. State and prove fundamental theorem of integral calculus.

Find the area of the region that lies inside the first curve and outside the second curve.
r2 = 18 cos 2θ, r = 3

Q. Intigrate
ʃ1/(1-x)3dx

Q. Intigrate
ʃ[x4/(x-1)(x+2)1/2]dx

Q. Intigrate
ʃ(sinx+cosx/tanx)dx

Find the reduction formula of ʃsec6xdx.