What is the integral from 0 to pi of (6e^x+8sin(x)) ?

The integral from 0 to pi of (6e^x+8sin(x)) is 6e^pi+10

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integral from 0 to pi of (6e^x+8sin(x))

\int_{0}^{π} (6 e^{x} + 8 sin (x)) d x

6 e^{π} + 10

Decimal

148.84415 \dots

Solution steps

\int_{0}^{π} 6 e^{x} + 8 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} 6 e^{x} d x + \int_{0}^{π} 8 sin (x) d x

\int_{0}^{π} 6 e^{x} d x = 6 (e^{π} - 1)

\int_{0}^{π} 8 sin (x) d x = 16

= 6 (e^{π} - 1) + 16

Simplify

6 (e^{π} - 1) + 16 : 6 e^{π} + 10

= 6 e^{π} + 10

\int_{1}^{3} \frac{2 ^{x}}{2 ^{x} + 4} d x

\int_{0}^{3} 3 + 2 y - y^{2} d y

\int_{- 2}^{2} \frac{3}{32} (4 - x^{2}) d x

\int_{0}^{1} \frac{2 x + 3}{x ^{2} + 1} d x

\int_{0}^{10} 0 d x

What is the integral from 0 to pi of (6e^x+8sin(x)) ?
The integral from 0 to pi of (6e^x+8sin(x)) is 6e^pi+10