Home
Class 12
MATHS
If f(x)=(sinx)/xAAx in (0,pi], prove tha...

If `f(x)=(sinx)/xAAx in (0,pi],` prove that `pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - III|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - 1|29 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi)(x)/(1+sinx)dx .

int_0^(pi/2) (x^2+x)dx

Show that int_0^pixf(sinx)dx=pi/2int_0^pif(sinx)dxdot

Show that int_0^pifx(sinx)dx=pi/2int_0^pif(sinx)dxdot

Prove that: int_0^(pi//2)(sin x)/(sinx-cosx)dx=pi/4

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

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

Prove that: int_0^(2a)f(x)dx=int_0^(2a)f(2a-x)dxdot

Prove that: int_(0)^(pi//2) (sinx)/(sinx +cos x)d dx =(pi)/(4)