What is the integral from-2 to 2 of x^4-8x^2+16 ?

The integral from-2 to 2 of x^4-8x^2+16 is 512/15

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integral from-2 to 2 of x^4-8x^2+16

\int_{- 2}^{2} x^{4} - 8 x^{2} + 16 d x

\frac{512}{15}

Decimal

34.13333 \dots

Solution steps

\int_{- 2}^{2} x^{4} - 8 x^{2} + 16 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} 8 x^{2} d x + \int_{- 2}^{2} 16 d x

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

\int_{- 2}^{2} 8 x^{2} d x = \frac{128}{3}

\int_{- 2}^{2} 16 d x = 64

= \frac{64}{5} - \frac{128}{3} + 64

Simplify

\frac{64}{5} - \frac{128}{3} + 64 : \frac{512}{15}

= \frac{512}{15}

What is the integral from-2 to 2 of x^4-8x^2+16 ?
The integral from-2 to 2 of x^4-8x^2+16 is 512/15