What is the integral from 0 to 4 of 3x^{1/2}-(2x-2) ?

The integral from 0 to 4 of 3x^{1/2}-(2x-2) is 8

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integral from 0 to 4 of 3x^{1/2}-(2x-2)

\int_{0}^{4} 3 x^{\frac{1}{2}} - (2 x - 2) d x

8

Solution steps

\int_{0}^{4} 3 x^{\frac{1}{2}} - (2 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}^{4} 3 x^{\frac{1}{2}} d x - \int_{0}^{4} 2 x - 2 d x

\int_{0}^{4} 3 x^{\frac{1}{2}} d x = 16

\int_{0}^{4} 2 x - 2 d x = 8

= 16 - 8

Simplify

= 8

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What is the integral from 0 to 4 of 3x^{1/2}-(2x-2) ?
The integral from 0 to 4 of 3x^{1/2}-(2x-2) is 8