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

The integral from-pi to pi of sin(x)sin(x) is pi

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integral from-pi to pi of sin(x)sin(x)

\int_{- π}^{π} sin (x) sin (x) d x

π

Decimal

3.14159 \dots

Solution steps

\int_{- π}^{π} sin (x) sin (x) d x

Simplify

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

= \int_{- π}^{π} sin^{2} (x) d x

Rewrite using trig identities

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

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (2 x) d x = 0

= \frac{1}{2} (2 π - 0)

Simplify

\frac{1}{2} (2 π - 0) : π

= π

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

\int_{2}^{8} u (x) d x

\int_{1}^{2} 9 x d x

\int_{- 4}^{4} ∣ x + 1 ∣ d x

\int_{\frac{π}{12}}^{\frac{π}{9}} sin (3 x) d x

What is the integral from-pi to pi of sin(x)sin(x) ?
The integral from-pi to pi of sin(x)sin(x) is pi