What is the integral from 0 to pi of 1+sin(t)cos(t) ?

The integral from 0 to pi of 1+sin(t)cos(t) is pi

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integral from 0 to pi of 1+sin(t)cos(t)

\int_{0}^{π} 1 + sin (t) cos (t) d t

π

Decimal

3.14159 \dots

Solution steps

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

\int_{0}^{π} 1 d t = π

\int_{0}^{π} sin (t) cos (t) d t = 0

= π + 0

Simplify

= π

What is the integral from 0 to pi of 1+sin(t)cos(t) ?
The integral from 0 to pi of 1+sin(t)cos(t) is pi