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

The integral from 0 to pi of 2sin(x)+sin(2x) is 4

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

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

4

Solution steps

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

\int_{0}^{π} 2 sin (x) d x = 4

\int_{0}^{π} sin (2 x) d x = 0

= 4 + 0

Simplify

= 4

t \to 3 lim (\frac{t ^{2}}{9 - t ^{2}})

x^{3}, 4

\frac{d}{d t} (\frac{sin ( t )}{t})

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

\int \frac{x + 3}{x ^{2} - 3 x + 2} d x

What is the integral from 0 to pi of 2sin(x)+sin(2x) ?
The integral from 0 to pi of 2sin(x)+sin(2x) is 4