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Popular >

integral from-1 to 3 of x(x^2-3)

Solution

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

Solution

8

Solution steps

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

Expand

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

= \int_{- 1}^{3} x^{3} - 3 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_{- 1}^{3} x^{3} d x - \int_{- 1}^{3} 3 x d x

\int_{- 1}^{3} x^{3} d x = 20

\int_{- 1}^{3} 3 x d x = 12

= 20 - 12

Simplify

= 8

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of x(x^2-3) ?
The integral from-1 to 3 of x(x^2-3) is 8