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

The integral from pi/6 to pi/2 of sin(2x) is 3/4

Popular >

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

\int_{\frac{π}{6}}^{\frac{π}{2}} sin (2 x) d x

\frac{3}{4}

Decimal Notation

0.75

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{2}} sin (2 x) d x

Apply u-substitution

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

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

Use the common integral:

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

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

Compute the boundaries:

\frac{3}{2}

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

Simplify

= \frac{3}{4}

\int_{- 1}^{2} x - 8 ∣ x ∣ d x

\int_{- 9}^{9} x 81 - x^{2} d x

\int_{0}^{s i n (x)} sin (t^{2}) d t

\int_{- 1}^{0} (x + 1) sin (nπ x) d x

What is the integral from pi/6 to pi/2 of sin(2x) ?
The integral from pi/6 to pi/2 of sin(2x) is 3/4