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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{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

\int_{- 1}^{1} t^{5} d t

integral from 0 to 2 of (8-2x^2)

\int_{0}^{2} (8 - 2 x^{2}) d x

integral from x to x^2 of t^3

\int_{x}^{x^{2}} t^{3} d t

integral from 0 to 3 of-x+3

\int_{0}^{3} - x + 3 d x

integral from 1 to 6 of |3x-9|

\int_{1}^{6} ∣ 3 x - 9 ∣ 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 1/3