What is the integral from pi/6 to pi/4 of sin(4t) ?

The integral from pi/6 to pi/4 of sin(4t) is 1/8

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integral from pi/6 to pi/4 of sin(4t)

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (4 t) d t

\frac{1}{8}

Decimal Notation

0.125

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (4 t) d t

Apply u-substitution

: \int_{\frac{2 π}{3}}^{π} sin (u) \frac{1}{4} d u

= \int_{\frac{2 π}{3}}^{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{2 π}{3}}^{π} sin (u) d u

Use the common integral:

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

= \frac{1}{4} [- cos (u)]_{\frac{2 π}{3}}^{π}

Compute the boundaries:

\frac{1}{2}

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

Simplify

= \frac{1}{8}

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What is the integral from pi/6 to pi/4 of sin(4t) ?
The integral from pi/6 to pi/4 of sin(4t) is 1/8