What is the integral from 0 to 1 of sin^2(2pix) ?

The integral from 0 to 1 of sin^2(2pix) is 1/2

Popular >

integral from 0 to 1 of sin^2(2pix)

\int_{0}^{1} sin^{2} (2 π x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{1} sin^{2} (2 π x) d x

Rewrite using trig identities

= \int_{0}^{1} \frac{1}{2} (1 - cos (4 π x)) 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}^{1} 1 - cos (4 π 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}^{1} 1 d x - \int_{0}^{1} cos (4 π x) d x)

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} cos (4 π x) d x = 0

= \frac{1}{2} (1 - 0)

Simplify

= \frac{1}{2}

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

\frac{\partial}{\partial x} (2 x y)

f (x) = (9 - 6 x^{2})^{2}

(2 x + y + 1) y^{^{'}} = 1

(x^{2} - 1)^{^{'}}

What is the integral from 0 to 1 of sin^2(2pix) ?
The integral from 0 to 1 of sin^2(2pix) is 1/2