Home
Class 12
MATHS
If f is an odd function, then evaluate ...

If `f` is an odd function, then evaluate `I=int_(-a)^a(f(sinx)/(f(cosx)+f(sin^2x)dx`

Text Solution

Verified by Experts

Let `phi(x)=(f(sinx))/(f(cosx)+f(sin^(2)x))`
`:.phi(-x)=(f(sin(-x)))/(f(cos(-x))+f(sin^(2)(-x)))`
`=(f(-sinx))/(f(cosx)+f(sin^(2)x))`
`=(-f(sinx))/(f(cosx)+f(sin^(2)x))=-phi(x)`
( `:.f` is an odd function)
`:.I=int_(a)^(a)(f(sinx))/(f(cosx)+f(sin^(2)x))dx=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) is an odd function, then the value of int_(-a)^(a)(f(sin x)/(f(cos x)+f(sin ^(2)x))) dx is equal to

If f is an odd function, show that: int_-a^a f(sinx)/(f(cosx)+f(sin^2x))dx=0

If f is an odd function and I=int_(-a)^(a)(f(sin x))/(f(cos x)+f (sin^(2)x))dx , then

The value of int_(-pi)^(pi) sinx f(cosx)dx is

Prove that int_-a^a f(x) dx=0 , where 'f' is an odd function. And, evaluate, int_-1^1 log[(2-x)/(2+x)] dx

Let f be an odd function then int_(-1)^(1) (|x| +f(x) cos x) dx is equal to

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Statement l If f satisfies f(x+y)=f(x)+f(y), AA x,y in R,then int_(-5) ^5 f(x)dx=0 Statement II: If f is an odd function, then int_(-a) ^a f(x) dx =0