What is the integral from 0 to 3 of (2x+sin(2pix)) ?

The integral from 0 to 3 of (2x+sin(2pix)) is 9

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integral from 0 to 3 of (2x+sin(2pix))

\int_{0}^{3} (2 x + sin (2 π x)) d x

9

Solution steps

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

\int_{0}^{3} 2 x d x = 9

\int_{0}^{3} sin (2 π x) d x = 0

= 9 + 0

Simplify

= 9

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What is the integral from 0 to 3 of (2x+sin(2pix)) ?
The integral from 0 to 3 of (2x+sin(2pix)) is 9