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

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\int_{0}^{3} (x^{2} - 2 x - 3) d x

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

\int_{- 1}^{1} x + ∣ x - 1 ∣ d x

\int_{0}^{20} x^{2} - 17 x + 70 d 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