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

The integral from 0 to pi of 4sin(x)+sin(4x) is 8

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

\int_{0}^{π} 4 sin (x) + sin (4 x) d x

8

Solution steps

\int_{0}^{π} 4 sin (x) + sin (4 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} 4 sin (x) d x + \int_{0}^{π} sin (4 x) d x

\int_{0}^{π} 4 sin (x) d x = 8

\int_{0}^{π} sin (4 x) d x = 0

= 8 + 0

Simplify

= 8

\frac{\partial}{\partial y} (1 - \frac{3}{x} + y)

x \to 0 lim (\frac{x ^{3} - 8}{x - 2})

\int e^{x} + 20 (1 + x^{2})^{- 1} d x

\frac{d}{d x} (sin (\frac{x}{4}))

x \to \frac{x}{2} lim (sin (x))

What is the integral from 0 to pi of 4sin(x)+sin(4x) ?
The integral from 0 to pi of 4sin(x)+sin(4x) is 8