What is the integral from-pi to pi of sin(mx)cos(nx) ?

The integral from-pi to pi of sin(mx)cos(nx) is 0

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integral from-pi to pi of sin(mx)cos(nx)

\int_{- π}^{π} sin (m x) cos (n x) d x

0

Solution steps

\int_{- π}^{π} sin (m x) cos (n x) d x

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

sin (m x) cos (n x) :

Odd

= 0

\int_{0}^{2} 6 - x^{2} - x d x

\int_{- 3}^{3} 2 x^{2} d x

\int_{4}^{- 4} (\frac{1}{2} x + 3) d x

\int_{0}^{c o s (x)} (x) d x

\int_{2}^{4} \frac{x}{( x + 1 ) ( x + 4 )} d x

What is the integral from-pi to pi of sin(mx)cos(nx) ?
The integral from-pi to pi of sin(mx)cos(nx) is 0