Home
Class 12
MATHS
int(0)^(pi//2)sinx sin2x sin3x sin 4x dx...

`int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=`

A

`(pi)/(4)`

B

`(pi)/(8)`

C

`(pi)/(16)`

D

`(pi)/(32)`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=int_(0)^(pi//2)cos x sin 2x cos3x sin 4x dx`
`rArr" "2I=int_(0)^(pi//2)cos2xsin2xsin4xdx`
`=(1)/(2)int_(0)^(pi//2)sin^(2)4xdx`
`=(1)/(2)int_(0)^(pi//2)(1-cos8x)/(2)dx`
`=(1)/(4)[x-(sin8x)/(8)]_(0)^(pi//2)=(pi)/(8)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Solve sinx +sin2x +sin3x +sin4x =0

Prove that int_(0)^((pi)/(2)) sin 2x log ( tan x ) dx = 0

If n is odd then int_(0)^(pi//2)sin^(n)x dx is

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

Evaluate int_(0)^((pi)/2)(sin3x)/(sinx+cosx) dx .

Evaluate: int_(-pi/2)^(pi/2)sin^2xcos^2x(sinx+cosx)dx

Evaluate the following : int_(0)^((pi)/(2))sin^(2) x cos^(4) x dx

Evaluate : int_(0)^(pi/2)(sin^(2)x + cos^(4)x)dx