What is the integral from 0 to pi/3 of sin(2x) ?

The integral from 0 to pi/3 of sin(2x) is 3/4

integral from 0 to pi/3 of sin(2x)

\int_{0}^{\frac{π}{3}} sin (2 x) d x

\frac{3}{4}

Decimal

0.75

Solution steps

\int_{0}^{\frac{π}{3}} sin (2 x) d x

Apply u-substitution

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

Use the common integral:

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

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

Compute the boundaries:

\frac{3}{2}

= \frac{1}{2} \cdot \frac{3}{2}

Simplify

= \frac{3}{4}

\frac{d}{d x} (ln (\frac{e ^{x} - 1}{e ^{x + 1}}))

\int_{0}^{2} (x - 7)^{2} d x

\int 3 a x d x

x \to 3 - lim (\frac{1}{x ^{2} - 9})

x \to 2 lim (\frac{4 - x ^{2}}{x})

What is the integral from 0 to pi/3 of sin(2x) ?
The integral from 0 to pi/3 of sin(2x) is 3/4