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Popular Calculus >

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

Solution

\int_{- 1}^{3} (2 x - x^{2}) d x

Solution

- \frac{4}{3}

+1

Decimal

- 1.33333 \dots

Solution steps

\int_{- 1}^{3} 2 x - x^{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_{- 1}^{3} 2 x d x - \int_{- 1}^{3} x^{2} d x

\int_{- 1}^{3} 2 x d x = 8

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

= 8 - \frac{28}{3}

Simplify

8 - \frac{28}{3} : - \frac{4}{3}

= - \frac{4}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of (2x-x^2) ?
The integral from-1 to 3 of (2x-x^2) is -4/3