What is the integral from 0 to pi/(32) of cos(8x) ?

The integral from 0 to pi/(32) of cos(8x) is 1/(8sqrt(2))

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integral from 0 to pi/(32) of cos(8x)

\int_{0}^{\frac{π}{32}} cos (8 x) d x

\frac{1}{8 2}

Decimal Notation

0.08838 \dots

Solution steps

\int_{0}^{\frac{π}{32}} cos (8 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{8} d u

= \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Use the common integral:

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

= \frac{1}{8} [sin (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{8} \cdot \frac{1}{2}

Simplify

= \frac{1}{8 2}

ln (2 - x)

n = 0 \sum \infty 6 (- \frac{1}{3})^{n}

\frac{\partial}{\partial x} (cos^{6} (x^{4} y^{5}))

\int 2 + x^{2} d x

x^{3} - 10 x^{2} + 12 x + 3

What is the integral from 0 to pi/(32) of cos(8x) ?
The integral from 0 to pi/(32) of cos(8x) is 1/(8sqrt(2))