What is the integral from 0 to 3 of (5+3cos(x)) ?

The integral from 0 to 3 of (5+3cos(x)) is 15+3sin(3)

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integral from 0 to 3 of (5+3cos(x))

\int_{0}^{3} (5 + 3 cos (x)) d x

15 + 3 sin (3)

Decimal Notation

15.42336 \dots

Solution steps

\int_{0}^{3} 5 + 3 cos (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} 5 d x + \int_{0}^{3} 3 cos (x) d x

\int_{0}^{3} 5 d x = 15

\int_{0}^{3} 3 cos (x) d x = 3 sin (3)

= 15 + 3 sin (3)

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What is the integral from 0 to 3 of (5+3cos(x)) ?
The integral from 0 to 3 of (5+3cos(x)) is 15+3sin(3)