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

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

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

\int_{0}^{1} cos^{2} (π x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{1} cos^{2} (π x) d x

Rewrite using trig identities

= \int_{0}^{1} 1 - sin^{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} (π x) d x

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

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

= 1 - \frac{1}{2}

Simplify

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

= \frac{1}{2}

\int \frac{2 - x}{x ^{2}} d x

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

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

\int_{0}^{1} 2 x 5^{x} d x

v^{\frac{3}{2}} (v + c e^{x})

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