What is the integral from 0 to pi of (8+3sin(x)) ?

The integral from 0 to pi of (8+3sin(x)) is 8pi+6

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integral from 0 to pi of (8+3sin(x))

\int_{0}^{π} (8 + 3 sin (x)) d x

8 π + 6

Decimal Notation

31.13274 \dots

Solution steps

\int_{0}^{π} 8 + 3 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} 8 d x + \int_{0}^{π} 3 sin (x) d x

\int_{0}^{π} 8 d x = 8 π

\int_{0}^{π} 3 sin (x) d x = 6

= 8 π + 6

\int_{0}^{1} (e^{- 2 x} + x - 1) d x

\int_{0}^{1} ln (3 x + 1) d x

\int_{x}^{x} e^{\frac{x}{y}} d y

\int_{- 1}^{5} (x^{3} - 3 x + 4) d x

\int_{0}^{3} \frac{1}{( 3 x + 4 ) ^{\frac{1}{3}}} d x

What is the integral from 0 to pi of (8+3sin(x)) ?
The integral from 0 to pi of (8+3sin(x)) is 8pi+6