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

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

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

\int_{0}^{π} sin (x) - sin (2 x) d x

2

Solution steps

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

\int_{0}^{π} sin (x) d x = 2

\int_{0}^{π} sin (2 x) d x = 0

= 2 - 0

Simplify

= 2

\int_{- 1}^{1} x^{3} + x + 2 d x

\int_{0}^{8} t^{3} - 10 t^{2} + 24 t d t

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

\int_{0}^{6} 2.8 x d x

\int_{0}^{π} (sin^{3} (θ)) d θ

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