Home
Class 12
MATHS
Prove that, int(0)^(pi)sinmxsinnxdx={{...

Prove that,
`int_(0)^(pi)sinmxsinnxdx={{:("0, when "mnen),((pi)/(2)", when m = n"):}`
where m and n are positive integers.

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(2)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise MCQ EXERCISE 9A|15 Videos
  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise VERY SHORT QUESTIONS|24 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos
  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Prove that, int_(0)^(pi)cos^(3)xdx=0

Prove that int_(-pi)^(pi)cosmxcosnxdx={{:(0,"when",mnen ne0),(pi,"when",m=n ne0),(2pi,"when",m=n=0):}

Prove that, int_(0)^(pi)f(sinx)dx=2int_(0)^((pi)/(2))f(sinx)dx .

Prove that, int_(0)^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx=pi^(2) .

Prove that, int_(0)^(6pi)sin^(4)xdx=6int_(0)^(pi)sin^(4)xdx

Prove that 2^(n) gt n for all positive integers n.

Prove that, int_(0)^((pi)/(2))cos^(n)x cos nx dx=(pi)/(2^(n+1)) .

Prove that, int_(-pi)^(pi)(xe^(x^(2)))/(1+x^(2))dx=0

Prove that: int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx = pi^2

Prove that, int_(0)^((pi)/(2))(sqrt(tanx)+sqrt(cotx))dx=sqrt(2)pi