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

The integral from 0 to pi of 3e^x-2sin(x) is 3e^pi-7

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

\int_{0}^{π} 3 e^{x} - 2 sin (x) d x

3 e^{π} - 7

Decimal

62.42207 \dots

Solution steps

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

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

\int_{0}^{π} 2 sin (x) d x = 4

= 3 (e^{π} - 1) - 4

Simplify

3 (e^{π} - 1) - 4 : 3 e^{π} - 7

= 3 e^{π} - 7

\int_{0}^{2} x ∣ x - 1 ∣ d x

\int_{0}^{1} e^{x} 1 - x d x

\int_{0}^{2} e^{x^{2} - x} d x

\int_{- 2}^{2} x^{2} + 3 d x

\int_{0}^{y} \frac{1}{y} d y

What is the integral from 0 to pi of 3e^x-2sin(x) ?
The integral from 0 to pi of 3e^x-2sin(x) is 3e^pi-7