What is the integral from-3 to 3 of (x^2-1)^2 ?

The integral from-3 to 3 of (x^2-1)^2 is 336/5

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integral from-3 to 3 of (x^2-1)^2

\int_{- 3}^{3} (x^{2} - 1)^{2} d x

\frac{336}{5}

Decimal Notation

67.2

Solution steps

\int_{- 3}^{3} (x^{2} - 1)^{2} d x

Expand

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

= \int_{- 3}^{3} 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_{- 3}^{3} x^{4} d x - \int_{- 3}^{3} 2 x^{2} d x + \int_{- 3}^{3} 1 d x

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

\int_{- 3}^{3} 2 x^{2} d x = 36

\int_{- 3}^{3} 1 d x = 6

= \frac{486}{5} - 36 + 6

Simplify

\frac{486}{5} - 36 + 6 : \frac{336}{5}

= \frac{336}{5}

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

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

What is the integral from-3 to 3 of (x^2-1)^2 ?
The integral from-3 to 3 of (x^2-1)^2 is 336/5