What is the integral from-2 to 2 of x^4+5x^2+2x+8 ?

The integral from-2 to 2 of x^4+5x^2+2x+8 is 1072/15

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integral from-2 to 2 of x^4+5x^2+2x+8

\int_{- 2}^{2} x^{4} + 5 x^{2} + 2 x + 8 d x

\frac{1072}{15}

Decimal

71.46666 \dots

Solution steps

\int_{- 2}^{2} x^{4} + 5 x^{2} + 2 x + 8 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} 5 x^{2} d x + \int_{- 2}^{2} 2 x d x + \int_{- 2}^{2} 8 d x

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

\int_{- 2}^{2} 5 x^{2} d x = \frac{80}{3}

\int_{- 2}^{2} 2 x d x = 0

\int_{- 2}^{2} 8 d x = 32

= \frac{64}{5} + \frac{80}{3} + 0 + 32

Simplify

\frac{64}{5} + \frac{80}{3} + 0 + 32 : \frac{1072}{15}

= \frac{1072}{15}

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What is the integral from-2 to 2 of x^4+5x^2+2x+8 ?
The integral from-2 to 2 of x^4+5x^2+2x+8 is 1072/15