What is the integral from 0 to pi/6 of sin(2x) ?

The integral from 0 to pi/6 of sin(2x) is 1/4

Popular >

integral from 0 to pi/6 of sin(2x)

\int_{0}^{\frac{π}{6}} sin (2 x) d x

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\int_{0}^{\frac{π}{6}} sin (2 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{3}} sin (u) \frac{1}{2} d u

= \int_{0}^{\frac{π}{3}} sin (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{3}} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{1}{2}

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

Simplify

= \frac{1}{4}

\int 3 x^{2} sin (3 x) d x

f (x) = 3^{x^{2} - 3}

\int \frac{1}{x ^{2} + 2 x + 2} d x

y = (3 x - x^{2}) (3 - x - x^{2})

3 y

What is the integral from 0 to pi/6 of sin(2x) ?
The integral from 0 to pi/6 of sin(2x) is 1/4