What is the integral from 0 to pi of 6sin(x)+sin(6x) ?

The integral from 0 to pi of 6sin(x)+sin(6x) is 12

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integral from 0 to pi of 6sin(x)+sin(6x)

\int_{0}^{π} 6 sin (x) + sin (6 x) d x

12

Solution steps

\int_{0}^{π} 6 sin (x) + sin (6 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} 6 sin (x) d x + \int_{0}^{π} sin (6 x) d x

\int_{0}^{π} 6 sin (x) d x = 12

\int_{0}^{π} sin (6 x) d x = 0

= 12 + 0

Simplify

= 12

x \to 4 + lim (\frac{6}{x - 4})

f (x) = x^{2} - 4 x - 5

\int (9 + x^{5})^{7} x^{4} d x

x \to 3 + lim (2 x^{2} - 4)

(3 y^{2} + 4 x) d x + (2 y x) d y = 0

What is the integral from 0 to pi of 6sin(x)+sin(6x) ?
The integral from 0 to pi of 6sin(x)+sin(6x) is 12