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

The integral from-2 to 2 of (x^2+3)^2 is 404/5

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

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

\frac{404}{5}

Decimal

80.8

Solution steps

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

Expand

(x^{2} + 3)^{2} : x^{4} + 6 x^{2} + 9

= \int_{- 2}^{2} x^{4} + 6 x^{2} + 9 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_{- 2}^{2} x^{4} d x + \int_{- 2}^{2} 6 x^{2} d x + \int_{- 2}^{2} 9 d x

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

\int_{- 2}^{2} 6 x^{2} d x = 32

\int_{- 2}^{2} 9 d x = 36

= \frac{64}{5} + 32 + 36

Simplify

\frac{64}{5} + 32 + 36 : \frac{404}{5}

= \frac{404}{5}

What is the integral from-2 to 2 of (x^2+3)^2 ?
The integral from-2 to 2 of (x^2+3)^2 is 404/5