What is the integral from 0 to pi of (2+sin(x)) ?

The integral from 0 to pi of (2+sin(x)) is 2pi+2

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integral from 0 to pi of (2+sin(x))

\int_{0}^{π} (2 + sin (x)) d x

2 π + 2

Decimal

8.28318 \dots

Solution steps

\int_{0}^{π} 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} 2 d x + \int_{0}^{π} sin (x) d x

\int_{0}^{π} 2 d x = 2 π

\int_{0}^{π} sin (x) d x = 2

= 2 π + 2

\int_{1}^{3} (x^{2} - 3 x) d x

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\int_{0}^{1} \frac{x}{1 + 5 x ^{2}} d x

\int_{0}^{1} \frac{10}{1 + x ^{2}} d x

What is the integral from 0 to pi of (2+sin(x)) ?
The integral from 0 to pi of (2+sin(x)) is 2pi+2