What is the integral from 0 to pi/(16) of cos(4x) ?

The integral from 0 to pi/(16) of cos(4x) is 1/(4sqrt(2))

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integral from 0 to pi/(16) of cos(4x)

\int_{0}^{\frac{π}{16}} cos (4 x) d x

\frac{1}{4 2}

Decimal

0.17677 \dots

Solution steps

\int_{0}^{\frac{π}{16}} cos (4 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{4} d u

= \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Use the common integral:

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

= \frac{1}{4} [sin (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{4} \cdot \frac{1}{2}

Simplify

= \frac{1}{4 2}

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What is the integral from 0 to pi/(16) of cos(4x) ?
The integral from 0 to pi/(16) of cos(4x) is 1/(4sqrt(2))