What is the integral from 0 to \sqrt[3]{4 of}(2sqrt(x)-x^2) ?

The integral from 0 to \sqrt[3]{4 of}(2sqrt(x)-x^2) is 4/3

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integral from 0 to \sqrt[3]{4 of}(2sqrt(x)-x^2)

\int_{0}^{34} (2 x - x^{2}) d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{0}^{34} 2 x - 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}^{34} 2 x d x - \int_{0}^{34} x^{2} d x

\int_{0}^{34} 2 x d x = \frac{8}{3}

\int_{0}^{34} x^{2} d x = \frac{4}{3}

= \frac{8}{3} - \frac{4}{3}

Simplify

\frac{8}{3} - \frac{4}{3} : \frac{4}{3}

= \frac{4}{3}

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\frac{\partial}{\partial x} (x^{4} + 6 y - 10)

What is the integral from 0 to \sqrt[3]{4 of}(2sqrt(x)-x^2) ?
The integral from 0 to \sqrt[3]{4 of}(2sqrt(x)-x^2) is 4/3