What is the integral from 0 to pi of cos^2(t) ?

The integral from 0 to pi of cos^2(t) is pi/2

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integral from 0 to pi of cos^2(t)

\int_{0}^{π} cos^{2} (t) d t

\frac{π}{2}

Solution steps

\int_{0}^{π} cos^{2} (t) d t

Rewrite using trig identities

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

Take the constant out:

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

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

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}^{π} 1 d t + \int_{0}^{π} cos (2 t) d t)

\int_{0}^{π} 1 d t = π

\int_{0}^{π} cos (2 t) d t = 0

= \frac{1}{2} (π + 0)

Simplify

\frac{1}{2} (π + 0) : \frac{π}{2}

= \frac{π}{2}

f (x) = x^{e^{x}}

\int (x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x

\int \frac{14 x - 13}{x ^{2} - 4 x - 21} d x

\frac{\partial}{\partial x} (\frac{7 y}{x ^{2} + y ^{2} + 19})

- \frac{18}{( x - 9 ) ^{2}}

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