What is the integral from 0 to 4 of sqrt(x)*(3-5x) ?

The integral from 0 to 4 of sqrt(x)*(3-5x) is -48

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integral from 0 to 4 of sqrt(x)*(3-5x)

\int_{0}^{4} x \cdot (3 - 5 x) d x

- 48

Solution steps

\int_{0}^{4} x (3 - 5 x) d x

Expand

x (3 - 5 x) : 3 x - 5 x^{\frac{3}{2}}

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

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

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

= 16 - 64

Simplify

= - 48

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What is the integral from 0 to 4 of sqrt(x)*(3-5x) ?
The integral from 0 to 4 of sqrt(x)*(3-5x) is -48