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

The integral from 0 to 4 of 2x-x^{3/2} is 16/5

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

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

\frac{16}{5}

Decimal

3.2

Solution steps

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

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

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= 16 - \frac{64}{5}

Simplify

16 - \frac{64}{5} : \frac{16}{5}

= \frac{16}{5}

What is the integral from 0 to 4 of 2x-x^{3/2} ?
The integral from 0 to 4 of 2x-x^{3/2} is 16/5