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Popular >

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

Solution

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

Solution

\frac{208}{15}

+1

Solution steps

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

Expand

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

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

\int_{0}^{4} 5 x d x = \frac{80}{3}

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

= \frac{80}{3} - \frac{64}{5}

Simplify

\frac{80}{3} - \frac{64}{5} : \frac{208}{15}

= \frac{208}{15}

Popular Examples

roots xe^y roots

x e^{y}

integral of 1/(sqrt(x^2+4x-5))

\int \frac{1}{x ^{2} + 4 x - 5} d x

t^{2} y^{^{'}} + 2 t y = y^{3}

y^'=(2sec(y))/((x-2)^2)

y^{^{'}} = \frac{2 sec ( y )}{( x - 2 ) ^{2}}

derivative of f(x)=(t^2+3)/(t^4-2t+4)derivative of

f (x) = \frac{t ^{2} + 3}{t ^{4} - 2 t + 4}

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of (5-x)sqrt(x) ?
The integral from 0 to 4 of (5-x)sqrt(x) is 208/15