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Popular Calculus >

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

Solution

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

Solution

\frac{5}{6}

+1

Decimal

0.83333 \dots

Solution steps

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

Expand

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

= \int_{1}^{2} 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_{1}^{2} x^{2} d x - \int_{1}^{2} x d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

= \frac{7}{3} - \frac{3}{2}

Simplify

\frac{7}{3} - \frac{3}{2} : \frac{5}{6}

= \frac{5}{6}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of x(x-1) ?
The integral from 1 to 2 of x(x-1) is 5/6