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Popular >

integral from 0 to 1 of x(x+5)

Solution

\int_{0}^{1} x (x + 5) d x

Solution

\frac{17}{6}

+1

Decimal Notation

2.83333 \dots

Solution steps

\int_{0}^{1} x (x + 5) d x

Expand

x (x + 5) : x^{2} + 5 x

= \int_{0}^{1} x^{2} + 5 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} 5 x d x

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

\int_{0}^{1} 5 x d x = \frac{5}{2}

= \frac{1}{3} + \frac{5}{2}

Simplify

\frac{1}{3} + \frac{5}{2} : \frac{17}{6}

= \frac{17}{6}

Popular Examples

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

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\int_{- 2}^{3} (x + 6 - x^{2}) d x

integral from 0 to pi of 9xcos(3x)

\int_{0}^{π} 9 x cos (3 x) d x

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\int_{0}^{2} 6 e^{x} d x

integral from 0 to 1 of x^{13}+13^x

\int_{0}^{1} x^{13} + 1 3^{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x(x+5) ?
The integral from 0 to 1 of x(x+5) is 17/6