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Popular >

integral from 0 to 1 of x-x^6

Solution

\int_{0}^{1} x - x^{6} d x

Solution

\frac{5}{14}

+1

Decimal Notation

0.35714 \dots

Solution steps

\int_{0}^{1} x - x^{6} 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^{6} d x

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

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= \frac{1}{2} - \frac{1}{7}

Simplify

\frac{1}{2} - \frac{1}{7} : \frac{5}{14}

= \frac{5}{14}

Popular Examples

integral from 2 to 5 of 3^{3x}

\int_{2}^{5} 3^{3 x} d x

integral from 1 to 2 of e^{1/x} 1/(x^2)

\int_{1}^{2} e^{\frac{1}{x}} \frac{1}{x ^{2}} d x

integral from 2 to 4 of (3x^2-2)

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

integral from 0 to 1 of 4^{3x}

\int_{0}^{1} 4^{3 x} d x

integral from-1 to x of 1-|x|

\int_{- 1}^{x} 1 - ∣ x ∣ d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x-x^6 ?
The integral from 0 to 1 of x-x^6 is 5/14