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Popular >

integral from 0 to 1 of x^4-x^2

Solution

\int_{0}^{1} x^{4} - x^{2} d x

Solution

- \frac{2}{15}

+1

Decimal

- 0.13333 \dots

Solution steps

\int_{0}^{1} x^{4} - x^{2} 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^{2} d x

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{1}{5} - \frac{1}{3}

Simplify

\frac{1}{5} - \frac{1}{3} : - \frac{2}{15}

= - \frac{2}{15}

Graph

Popular Examples

integral from 0 to pi/4 of 1 (cos^4(x))

\int_{0}^{\frac{π}{4}} \frac{d}{1} (cos^{4} (x)) d x

integral from 2 to 6 of (x^2+7x-5)(x-2)

\int_{2}^{6} (x^{2} + 7 x - 5) (x - 2) d x

integral from 1 to 2 of (x-1)(2-x)

\int_{1}^{2} (x - 1) (2 - x) d x

integral from-pi/4 to pi/4 of sin^2(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin^{2} (x) d x

integral from 0 to 3 of 4xe^{x^2}

\int_{0}^{3} 4 x e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^4-x^2 ?
The integral from 0 to 1 of x^4-x^2 is -2/15