What is the integral from 0 to pi/(12) of sin(6x) ?

The integral from 0 to pi/(12) of sin(6x) is 1/6

Popular >

integral from 0 to pi/(12) of sin(6x)

\int_{0}^{\frac{π}{12}} sin (6 x) d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{0}^{\frac{π}{12}} sin (6 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{2}} sin (u) \frac{1}{6} d u

= \int_{0}^{\frac{π}{2}} sin (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{0}^{\frac{π}{2}} sin (u) d u

Use the common integral:

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

= \frac{1}{6} [- cos (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= \frac{1}{6} \cdot 1

Simplify

= \frac{1}{6}

\int_{- 1}^{2} \frac{3}{x ^{4}} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x)) d x

\int_{0}^{1} (2 x^{4} - 3 x^{2} + 5) d x

\int_{1}^{2} \frac{5 - 6 x}{x ^{3}} d x

\int_{1}^{2} x ln (x^{2}) d x

What is the integral from 0 to pi/(12) of sin(6x) ?
The integral from 0 to pi/(12) of sin(6x) is 1/6