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

The integral from-pi to pi of cos(mx) is (2sin(pim))/m

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integral from-pi to pi of cos(mx)

\int_{- π}^{π} cos (m x) d x

\frac{2 sin ( πm )}{m}

Solution steps

\int_{- π}^{π} cos (m x) d x

Apply u-substitution

: \int_{- πm}^{mπ} \frac{cos ( u )}{m} d u

= \int_{- πm}^{mπ} \frac{cos ( u )}{m} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{m} \cdot \int_{- πm}^{mπ} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{m} [sin (u)]_{- πm}^{mπ}

Compute the boundaries:

2 sin (πm)

= \frac{1}{m} \cdot 2 sin (πm)

Simplify

= \frac{2 sin ( πm )}{m}

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What is the integral from-pi to pi of cos(mx) ?
The integral from-pi to pi of cos(mx) is (2sin(pim))/m