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

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

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

\int_{0}^{π} 2 + cos^{2} (t) d t

2 π + \frac{π}{2}

Decimal Notation

7.85398 \dots

Solution steps

\int_{0}^{π} 2 + 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

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

\int_{0}^{π} 2 d t = 2 π

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

= 2 π + \frac{π}{2}

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