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Popular >

integral from 1 to 3 of-x^2+x

Solution

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

Solution

- \frac{14}{3}

+1

Decimal Notation

- 4.66666 \dots

Solution steps

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} x d x = 4

= - \frac{26}{3} + 4

Simplify

- \frac{26}{3} + 4 : - \frac{14}{3}

= - \frac{14}{3}

Popular Examples

integral from 0 to pi of cos(x)x

\int_{0}^{π} cos (x) x d x

integral from pi to 0 of cos(x)

\int_{π}^{0} cos (x) d x

integral from 1 to 8 of 4x^{1/3}

\int_{1}^{8} 4 x^{\frac{1}{3}} d x

integral from 2 to 4 of x^2-3x+4

\int_{2}^{4} x^{2} - 3 x + 4 d x

integral from 1 to 2 of (y^2+1)/(y^2)

\int_{1}^{2} \frac{y ^{2} + 1}{y ^{2}} d y

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of-x^2+x ?
The integral from 1 to 3 of-x^2+x is -14/3