What is the integral from pi/8 to pi/4 of sin(4x) ?

The integral from pi/8 to pi/4 of sin(4x) is 1/4

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integral from pi/8 to pi/4 of sin(4x)

\int_{\frac{π}{8}}^{\frac{π}{4}} sin (4 x) d x

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{\frac{π}{8}}^{\frac{π}{4}} sin (4 x) d x

Apply u-substitution

= \int_{\frac{π}{2}}^{π} sin (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_{\frac{π}{2}}^{π} sin (u) d u

Use the common integral:

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

= \frac{1}{4} [- cos (u)]_{\frac{π}{2}}^{π}

Compute the boundaries:

1

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

Simplify

= \frac{1}{4}

What is the integral from pi/8 to pi/4 of sin(4x) ?
The integral from pi/8 to pi/4 of sin(4x) is 1/4