Home
Class 12
MATHS
The value of the integral int(0)^(1)(x^(...

The value of the integral `int_(0)^(1)(x^(3))/(1+x^(8))dx` is

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`(pi)/(8)`

D

`(pi)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
D
Put `x^(4)=t` and `4x^(3)dx=dt`.
`[x=0impliest=0]` and `[x=1impliest=1]`
`:. I=(1)/(4)int_(0)^(1)(dt)/((1+t^(2)))=(1)/(4)[tan^(-1)t]_(0)^(1)=(1)/(4)[tan^(-1)-tan^(-1)0]=((1)/(4)xx(pi)/(4))=(pi)/(16)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RS AGGARWAL|Exercise Exercise 16D|17 Videos

  • CROSS,OR VECTOR, PRODUCT OF VECTORS

    RS AGGARWAL|Exercise Exercise 24|26 Videos

  • DETERMINANTS

    RS AGGARWAL|Exercise Objective Questions|29 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_(0)^(1)(sqrt(x))/(1+x^(2))dx is

The value of the integral int_(0)^(4)(x^(2))/(x^(2)-4x+8)dx is equal to

The value of the integral int_(-a)^(a)(e^(x))/(1+e^(x))dx is

The value of the integral int_(0)^(oo)(1)/(1+x^(4))dx is

The value of the integral int_(0)^(1)sin^(-1)(3x-4x^(3))dx is

The value of the integral int_(0)^(8)(x^(2))/(x^(2)+8x+32) dx is equal to

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

The value of the integral int_(0)^(2)|x^(2)-1|dx is

If f(x)-3cos(tan^(-1)x) , then the value of the integral int_(0)^(1)xf''(x)dx is