What is the integral from 0 to pi/2 of 7sin(t)-2cos(t) ?

The integral from 0 to pi/2 of 7sin(t)-2cos(t) is 5

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integral from 0 to pi/2 of 7sin(t)-2cos(t)

\int_{0}^{\frac{π}{2}} 7 sin (t) - 2 cos (t) d t

5

Solution steps

\int_{0}^{\frac{π}{2}} 7 sin (t) - 2 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}^{\frac{π}{2}} 7 sin (t) d t - \int_{0}^{\frac{π}{2}} 2 cos (t) d t

\int_{0}^{\frac{π}{2}} 7 sin (t) d t = 7

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

= 7 - 2

Simplify

= 5

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What is the integral from 0 to pi/2 of 7sin(t)-2cos(t) ?
The integral from 0 to pi/2 of 7sin(t)-2cos(t) is 5