What is the integral from 0 to 8 of 12-4\sqrt[3]{x} ?

The integral from 0 to 8 of 12-4\sqrt[3]{x} is 48

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integral from 0 to 8 of 12-4\sqrt[3]{x}

\int_{0}^{8} 12 - 4 3 x d x

48

Solution steps

\int_{0}^{8} 12 - 4 3 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}^{8} 12 d x - \int_{0}^{8} 4 3 x d x

\int_{0}^{8} 12 d x = 96

\int_{0}^{8} 4 3 x d x = 48

= 96 - 48

Simplify

= 48

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\int_{- 1}^{0} - 3 - x^{3} + 3 - x d x

What is the integral from 0 to 8 of 12-4\sqrt[3]{x} ?
The integral from 0 to 8 of 12-4\sqrt[3]{x} is 48