What is the integral from 0 to pi of sin(x)*sin(x) ?

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

Popular >

integral from 0 to pi of sin(x)*sin(x)

\int_{0}^{π} sin (x) \cdot sin (x) d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{π} sin (x) sin (x) d x

Simplify

sin (x) sin (x) : sin^{2} (x)

= \int_{0}^{π} sin^{2} (x) d x

Rewrite using trig identities

= \int_{0}^{π} \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{π} 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{π} 1 d x - \int_{0}^{π} cos (2 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= \frac{1}{2} (π - 0)

Simplify

\frac{1}{2} (π - 0) : \frac{π}{2}

= \frac{π}{2}

\int_{4}^{8} \frac{1}{x - 4} d x

\int_{0}^{1} 4 x + 1 d x

\int_{1}^{2} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

\int_{4}^{25} \frac{1}{x} d x

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

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