What is the integral from 0 to pi/2 of 3e^x-3cos(x) ?

The integral from 0 to pi/2 of 3e^x-3cos(x) is 3e^{pi/2}-6

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integral from 0 to pi/2 of 3e^x-3cos(x)

\int_{0}^{\frac{π}{2}} 3 e^{x} - 3 cos (x) d x

3 e^{\frac{π}{2}} - 6

Decimal Notation

8.43143 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 3 e^{x} - 3 cos (x) d x

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}} 3 e^{x} d x - \int_{0}^{\frac{π}{2}} 3 cos (x) d x

\int_{0}^{\frac{π}{2}} 3 e^{x} d x = 3 (e^{\frac{π}{2}} - 1)

\int_{0}^{\frac{π}{2}} 3 cos (x) d x = 3

= 3 (e^{\frac{π}{2}} - 1) - 3

Simplify

3 (e^{\frac{π}{2}} - 1) - 3 : 3 e^{\frac{π}{2}} - 6

= 3 e^{\frac{π}{2}} - 6

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What is the integral from 0 to pi/2 of 3e^x-3cos(x) ?
The integral from 0 to pi/2 of 3e^x-3cos(x) is 3e^{pi/2}-6