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Popular >

integral from 0 to 1 of (x^2+x)

Solution

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

Solution

\frac{5}{6}

+1

Decimal

0.83333 \dots

Solution steps

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

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

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

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

Simplify

\frac{1}{3} + \frac{1}{2} : \frac{5}{6}

= \frac{5}{6}

Graph

Popular Examples

integral from 2 to 3 of 1/(sqrt(x-2))

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

integral from 0 to 2 of pi(x^3)^2

\int_{0}^{2} π (x^{3})^{2} d x

integral from 0 to pi of sin(θ)cos^2(θ)

\int_{0}^{π} sin (θ) cos^{2} (θ) d θ

integral from 0 to pi of sin(5x+pi)

\int_{0}^{π} sin (5 x + π) d x

integral from 1 to 2 of sqrt(1+x^2)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x^2+x) ?
The integral from 0 to 1 of (x^2+x) is 5/6