`n|sinx|= m |cos|` in` [0, 2pi]` where n > m and are positive integers

Evaluate the following integrals: intsin mx cos nx dx where m and n are distinct positive integers.

Evaluate int sinmx sin nx dx , where m and n are positive integers. What happens if m=n?

The number of all pairs (m, n), where m and n are positive integers, such that 1/(m)+1/(n)+1/(mn)=2/(5) is

Evaluate the integerals. f cos mx cos nx dx on R, m ne n, m and n are positive integers.

Evaluate int cosmx cosnx dx , where m,n are positive integers and m ne n . What happens if m=n?

The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive integer)

The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive integer)

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

Evaluate int cos mx cos nxdx where m,n are positive integers,m!=n What happens if m=n?

Show that int_(0)^(n pi+v)|sin x|dx=2n+1-cos v, where n is a positive integer and ,0<=v