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Popular Calculus >

integral from 0 to 1 of x-x^5

Solution

\int_{0}^{1} x - x^{5} d x

Solution

\frac{1}{3}

+1

Decimal

0.33333 \dots

Solution steps

\int_{0}^{1} x - x^{5} 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 d x - \int_{0}^{1} x^{5} d x

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

\int_{0}^{1} x^{5} d x = \frac{1}{6}

= \frac{1}{2} - \frac{1}{6}

Simplify

\frac{1}{2} - \frac{1}{6} : \frac{1}{3}

= \frac{1}{3}

Graph

Popular Examples

integral from-1 to 1 of t^5

integral from 0 to 3 of-x+3

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

integral from 0 to 1 of (3x+5)^6

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 1/3