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Popular >

integral from 0 to 1 of (x^3-x)

Solution

\int_{0}^{1} (x^{3} - x) d x

Solution

- \frac{1}{4}

+1

Decimal Notation

- 0.25

Solution steps

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

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

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

= \frac{1}{4} - \frac{1}{2}

Simplify

\frac{1}{4} - \frac{1}{2} : - \frac{1}{4}

= - \frac{1}{4}

Popular Examples

integral from 2 to x of 1/(1+t^4)

\int_{2}^{x} \frac{1}{1 + t ^{4}} d t

integral from-2 to 2 of 8-2x^2

\int_{- 2}^{2} 8 - 2 x^{2} d x

integral from-3 to 3 of |x^2-4|

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

integral from 0 to 1 of (2e^{x/3+4}+5)

\int_{0}^{1} (2 e^{\frac{x}{3} + 4} + 5) d x

integral from 0 to 4 of 2x^2

\int_{0}^{4} 2 x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x^3-x) ?
The integral from 0 to 1 of (x^3-x) is -1/4