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

The integral from 0 to (3pi)/2 of 2+2sin(x) is 3pi+2

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

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

3 π + 2

Decimal Notation

11.42477 \dots

Solution steps

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

\int_{0}^{\frac{3 π}{2}} 2 d x = 3 π

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

= 3 π + 2

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