What is the integral from-2pi to pi of sin^2(x) ?

The integral from-2pi to pi of sin^2(x) is (3pi)/2

Popular >

integral from-2pi to pi of sin^2(x)

\int_{- 2 π}^{π} sin^{2} (x) d x

\frac{3 π}{2}

Decimal

4.71238 \dots

Solution steps

\int_{- 2 π}^{π} sin^{2} (x) d x

Rewrite using trig identities

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

\int_{- 2 π}^{π} 1 d x = 3 π

\int_{- 2 π}^{π} cos (2 x) d x = 0

= \frac{1}{2} (3 π - 0)

Simplify

\frac{1}{2} (3 π - 0) : \frac{3 π}{2}

= \frac{3 π}{2}

x \to 3 lim (\frac{ln ( x ) - ln ( 3 )}{x - 3})

n = 0 \sum \infty e^{- n^{2}}

\frac{\partial}{\partial x} (z^{3} x)

\int 5 sec (x + 3) tan (x + 3) d x

x y^{^{'}} + 3 y = 4 x, y (3) = 6

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