If int(0)^(pi) x f (cos^(2) x + tan ^(4)...

If `int_(0)^(pi) x f (cos^(2) x + tan ^(4) x ) dx`
`= k int_(0)^(pi//2) f(cos^(2) x + tan ^(4) x ) dx` then k =

Text Solution

Verified by Experts

The correct Answer is:

`19.97`

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Knowledge Check

If I_(1)= int_(0)^(3pi) f (cos^(2) x)dx and I_(2)= int_(0)^(x) f [cos^(2)x] dx , then

A

`I_(1)= I_(2)`

B

`I_(1)= 2I_(2)`

C

`I_(1)= 5I_(2)`

D

`I_(1)= 3I_(2)`

If int_(0)^(npi) f(cos^(2)x)dx=k int_(0)^(pi) f(cos^(2)x)dx , then the value of k, is

A

1

B

n

C

`n//2`

D

none of these

int_(0)^(pi//4)e^(x)(1+tan x + tan^(2)x)dx=

A

tan 1

B

e. tan 1

C

`e^(pi//4)`

D

tan e

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