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Popular >

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

Solution

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

Solution

\frac{5}{6}

+1

Solution steps

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

Expand

x (x + 1) : x^{2} + x

= \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}

Popular Examples

integral from 0 to pi of 2

\int_{0}^{π} 2 d x

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

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

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

integral from 2 to 3 of 4-x^2

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

Frequently Asked Questions (FAQ)

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