What is the integral from-4 to 0 of 3x^2+x^3-4x ?

The integral from-4 to 0 of 3x^2+x^3-4x is 32

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integral from-4 to 0 of 3x^2+x^3-4x

\int_{- 4}^{0} 3 x^{2} + x^{3} - 4 x d x

32

Solution steps

\int_{- 4}^{0} 3 x^{2} + x^{3} - 4 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_{- 4}^{0} 3 x^{2} d x + \int_{- 4}^{0} x^{3} d x - \int_{- 4}^{0} 4 x d x

\int_{- 4}^{0} 3 x^{2} d x = 64

\int_{- 4}^{0} x^{3} d x = - 64

\int_{- 4}^{0} 4 x d x = - 32

= 64 - 64 - (- 32)

Simplify

= 32

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What is the integral from-4 to 0 of 3x^2+x^3-4x ?
The integral from-4 to 0 of 3x^2+x^3-4x is 32