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Popular >

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

Solution

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

Solution

- \frac{1}{6}

+1

Decimal Notation

- 0.16666 \dots

Solution steps

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

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

\int_{- 1}^{0} 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}

Popular Examples

integral from 0 to pi/2 of sin(φ)

\int_{0}^{\frac{π}{2}} sin (φ) d φ

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

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

integral from-3 to 2 of (12-x^2-x)

\int_{- 3}^{2} (12 - x^{2} - x) d x

integral from 1 to 2.5 of x

\int_{1}^{2.5} x d x

integral from x^2 to sqrt(x of)xy

\int_{x^{2}}^{x} x y d y

Frequently Asked Questions (FAQ)

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