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

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

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

\int_{0}^{1} cos^{2} (2 π x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{1} cos^{2} (2 π x) d x

Rewrite using trig identities

= \int_{0}^{1} 1 - sin^{2} (2 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

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

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

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

= 1 - \frac{1}{2}

Simplify

1 - \frac{1}{2} : \frac{1}{2}

= \frac{1}{2}

\frac{d}{d x} (x^{0.5} + 2 x^{- 0.5})

(2.6) (- 3.5)

4 sin (3 x)

\int \frac{2 - x}{4 x ^{2} + 4 x - 3} d x

\frac{d y}{d x} + x^{2} (3 y - 2) = 0

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