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Popular >

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

Popular Examples

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\int_{0}^{3} (3 e^{2 x} - x^{2}) d x

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\int_{0}^{1} 2 y e^{y} d y

integral from-1 to 2 of ((2-x^2)-(-x))

\int_{- 1}^{2} ((2 - x^{2}) - (- x)) d x

integral from 1 to 9 of 1/((x-1)^{2/3)}

\int_{1}^{9} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

integral from 0 to t of 3t^3

\int_{0}^{t} 3 t^{3} d t

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