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

The integral from-3 to 3 of (x^2-2)^2 is 246/5

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

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

\frac{246}{5}

Decimal

49.2

Solution steps

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

Expand

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

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

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

\int_{- 3}^{3} 4 x^{2} d x = 72

\int_{- 3}^{3} 4 d x = 24

= \frac{486}{5} - 72 + 24

Simplify

\frac{486}{5} - 72 + 24 : \frac{246}{5}

= \frac{246}{5}

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What is the integral from-3 to 3 of (x^2-2)^2 ?
The integral from-3 to 3 of (x^2-2)^2 is 246/5