What is the integral from-1 to 1 of cos(wx) ?

The integral from-1 to 1 of cos(wx) is (2sin(w))/w

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integral from-1 to 1 of cos(wx)

\int_{- 1}^{1} cos (w x) d x

\frac{2 sin ( w )}{w}

Solution steps

\int_{- 1}^{1} cos (w x) d x

Apply u-substitution

: \int_{- w}^{w} \frac{cos ( u )}{w} d u

= \int_{- w}^{w} \frac{cos ( u )}{w} d u

Take the constant out:

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

= \frac{1}{w} \cdot \int_{- w}^{w} cos (u) d u

Use the common integral:

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

= \frac{1}{w} [sin (u)]_{- w}^{w}

Compute the boundaries:

2 sin (w)

= \frac{1}{w} \cdot 2 sin (w)

Simplify

= \frac{2 sin ( w )}{w}

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What is the integral from-1 to 1 of cos(wx) ?
The integral from-1 to 1 of cos(wx) is (2sin(w))/w