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

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

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integral from-pi/2 to pi/2 of 2t+cos(t)

\int_{- \frac{π}{2}}^{\frac{π}{2}} 2 t + cos (t) d t

2

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} 2 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_{- \frac{π}{2}}^{\frac{π}{2}} 2 t d t + \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (t) d t

\int_{- \frac{π}{2}}^{\frac{π}{2}} 2 t d t = 0

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

= 0 + 2

Simplify

= 2

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