What is the integral from-2 to 4 of x^2(x^3+8) ?

The integral from-2 to 4 of x^2(x^3+8) is 864

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integral from-2 to 4 of x^2(x^3+8)

\int_{- 2}^{4} x^{2} (x^{3} + 8) d x

864

Solution steps

\int_{- 2}^{4} x^{2} (x^{3} + 8) d x

Expand

x^{2} (x^{3} + 8) : x^{5} + 8 x^{2}

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

\int_{- 2}^{4} x^{5} d x = 672

\int_{- 2}^{4} 8 x^{2} d x = 192

= 672 + 192

Simplify

= 864

What is the integral from-2 to 4 of x^2(x^3+8) ?
The integral from-2 to 4 of x^2(x^3+8) is 864