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Popular >

integral from 0 to 1 of x^4-x^5

Solution

\int_{0}^{1} x^{4} - x^{5} d x

Solution

\frac{1}{30}

+1

Decimal Notation

0.03333 \dots

Solution steps

\int_{0}^{1} x^{4} - 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^{4} d x - \int_{0}^{1} x^{5} d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

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

= \frac{1}{5} - \frac{1}{6}

Simplify

\frac{1}{5} - \frac{1}{6} : \frac{1}{30}

= \frac{1}{30}

Popular Examples

integral from 1 to 3 of sqrt(x^2+3)

\int_{1}^{3} x^{2} + 3 d x

integral from 1 to 4 of 3^{x-1}

\int_{1}^{4} 3^{x - 1} d x

integral from 1 to 3 of 5/x

\int_{1}^{3} \frac{5}{x} d x

integral from-3 to 2 of x^2+x-6

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

integral from 0 to 2 of (4x+8)/(x^2+4)

\int_{0}^{2} \frac{4 x + 8}{x ^{2} + 4} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^4-x^5 ?
The integral from 0 to 1 of x^4-x^5 is 1/30