What is the integral from 0 to 4 of x(sqrt(x)-1) ?

The integral from 0 to 4 of x(sqrt(x)-1) is 24/5

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integral from 0 to 4 of x(sqrt(x)-1)

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

\frac{24}{5}

Decimal

4.8

Solution steps

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

Expand

x (x - 1) : x^{\frac{3}{2}} - x

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

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

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

= \frac{64}{5} - 8

Simplify

\frac{64}{5} - 8 : \frac{24}{5}

= \frac{24}{5}

x y^{^{'}} + y = 6 x y^{2}

\frac{\partial}{\partial t} (s + 2 t)

\int_{0}^{7} x d x

\int (x^{2} + e^{1 - x}) d x

y^{^{''}} + 2 y + y = x e^{- x}

What is the integral from 0 to 4 of x(sqrt(x)-1) ?
The integral from 0 to 4 of x(sqrt(x)-1) is 24/5