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

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

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

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

\frac{512}{15}

Decimal

34.13333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{512}{15}

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