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Popular >

integral from 0 to 1 of x^2-x

Solution

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

Solution

- \frac{1}{6}

+1

Decimal Notation

- 0.16666 \dots

Solution steps

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

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

= \frac{1}{3} - \frac{1}{2}

Simplify

\frac{1}{3} - \frac{1}{2} : - \frac{1}{6}

= - \frac{1}{6}

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\frac{d}{d x} (x^{3} - x^{2} - x)

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\frac{d}{d x} (x^{4} - 2 x)

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^2-x ?
The integral from 0 to 1 of x^2-x is -1/6