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Popular Calculus >

integral from 0 to 5 of (x^3-x)

Solution

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

Solution

\frac{575}{4}

+1

Decimal

143.75

Solution steps

\int_{0}^{5} x^{3} - 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}^{5} x^{3} d x - \int_{0}^{5} x d x

\int_{0}^{5} x^{3} d x = \frac{625}{4}

\int_{0}^{5} x d x = \frac{25}{2}

= \frac{625}{4} - \frac{25}{2}

Simplify

\frac{625}{4} - \frac{25}{2} : \frac{575}{4}

= \frac{575}{4}

Graph

Popular Examples

integral from-1 to 1 of x/((x+3)^2)

integral from 0 to 1 of sqrt(1-x^2)*x

integral from 1 to 5 of e^{-x}

integral from 0 to 25 of 7/(sqrt(25-x))

integral from 1 to 2 of 2/((3x-2)^3)

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of (x^3-x) ?
The integral from 0 to 5 of (x^3-x) is 575/4