What is the integral from 0 to 30 of 82+4sin(x/2) ?

The integral from 0 to 30 of 82+4sin(x/2) is -8cos(15)+2468

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integral from 0 to 30 of 82+4sin(x/2)

\int_{0}^{30} 82 + 4 sin (\frac{x}{2}) d x

- 8 cos (15) + 2468

Decimal Notation

2474.07750 \dots

Solution steps

\int_{0}^{30} 82 + 4 sin (\frac{x}{2}) 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}^{30} 82 d x + \int_{0}^{30} 4 sin (\frac{x}{2}) d x

\int_{0}^{30} 82 d x = 2460

\int_{0}^{30} 4 sin (\frac{x}{2}) d x = 8 (- cos (15) + 1)

= 2460 + 8 (- cos (15) + 1)

Simplify

2460 + 8 (- cos (15) + 1) : - 8 cos (15) + 2468

= - 8 cos (15) + 2468

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What is the integral from 0 to 30 of 82+4sin(x/2) ?
The integral from 0 to 30 of 82+4sin(x/2) is -8cos(15)+2468