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Popular Calculus >

integral from-1 to 0 of x+x^2

Solution

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

Solution

- \frac{1}{6}

+1

Decimal

- 0.16666 \dots

Solution steps

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

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

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

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

Simplify

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

= - \frac{1}{6}

Graph

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Frequently Asked Questions (FAQ)

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