What is the integral from 0 to 1 of (x^2-1)^2 ?

The integral from 0 to 1 of (x^2-1)^2 is 8/15

Popular >

integral from 0 to 1 of (x^2-1)^2

\int_{0}^{1} (x^{2} - 1)^{2} d x

\frac{8}{15}

Decimal

0.53333 \dots

Solution steps

\int_{0}^{1} (x^{2} - 1)^{2} d x

Expand

(x^{2} - 1)^{2} : x^{4} - 2 x^{2} + 1

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

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

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

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

= \frac{1}{5} - \frac{2}{3} + 1

Simplify

\frac{1}{5} - \frac{2}{3} + 1 : \frac{8}{15}

= \frac{8}{15}

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

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

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

\int_{0}^{π} sin^{2} (t) cos (t) d t

\int_{- \infty}^{0} e^{x - e^{x}} d x

What is the integral from 0 to 1 of (x^2-1)^2 ?
The integral from 0 to 1 of (x^2-1)^2 is 8/15