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Popular Calculus >

integral from 0 to 1 of x^3-x

Solution

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

Solution

- \frac{1}{4}

+1

Decimal

- 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}

Graph

Popular Examples

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

\int_{0}^{2} \frac{1}{1 + e ^{1 - x}} d x

integral from 0 to pi/2 of xcos^2(x)

\int_{0}^{\frac{π}{2}} x cos^{2} (x) d x

integral from 0 to 3 of |x^2-1|

\int_{0}^{3} x^{2} - 1 d x

integral from 1 to 7 of 1/(x^2)

\int_{1}^{7} \frac{1}{x ^{2}} d x

integral from 1 to 4 of sqrt(u)

\int_{1}^{4} u d u

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