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Popular Calculus >

integral from 0 to 6 of x(x^2-9)

Solution

\int_{0}^{6} x (x^{2} - 9) d x

Solution

162

Solution steps

\int_{0}^{6} x (x^{2} - 9) d x

Expand

x (x^{2} - 9) : x^{3} - 9 x

= \int_{0}^{6} x^{3} - 9 x 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_{0}^{6} x^{3} d x - \int_{0}^{6} 9 x d x

\int_{0}^{6} x^{3} d x = 324

\int_{0}^{6} 9 x d x = 162

= 324 - 162

Simplify

= 162

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of x(x^2-9) ?
The integral from 0 to 6 of x(x^2-9) is 162