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Popular Calculus >

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

Solution

\int_{0}^{1} x (x^{2} - 1) d x

Solution

- \frac{1}{4}

+1

Decimal

- 0.25

Solution steps

\int_{0}^{1} x (x^{2} - 1) d x

Expand

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

= \int_{0}^{1} 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}^{1} x^{3} d x - \int_{0}^{1} x d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{1}{4} - \frac{1}{2}

Simplify

\frac{1}{4} - \frac{1}{2} : - \frac{1}{4}

= - \frac{1}{4}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x^2-1) ?
The integral from 0 to 1 of x(x^2-1) is -1/4