What is the integral from 0 to pi/2 of picos^2(x) ?

The integral from 0 to pi/2 of picos^2(x) is (pi^2)/4

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integral from 0 to pi/2 of picos^2(x)

\int_{0}^{\frac{π}{2}} π cos^{2} (x) d x

\frac{π ^{2}}{4}

Solution steps

\int_{0}^{\frac{π}{2}} π cos^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{\frac{π}{2}} cos^{2} (x) d x

Rewrite using trig identities

= π \cdot \int_{0}^{\frac{π}{2}} \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

= π \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 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

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

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

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

= π \frac{1}{2} (\frac{π}{2} + 0)

Simplify

π \frac{1}{2} (\frac{π}{2} + 0) : \frac{π ^{2}}{4}

= \frac{π ^{2}}{4}

\int \frac{x + 9}{x ^{2} + 4} d x

x \to \infty lim ((x!)^{2})

x^{2} - 12, 4 x

y = (x + 3)^{3}, at x = - \frac{1}{75}

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

What is the integral from 0 to pi/2 of picos^2(x) ?
The integral from 0 to pi/2 of picos^2(x) is (pi^2)/4