What is the integral from 0 to 2 of 12x^3+3x^2-4x ?

The integral from 0 to 2 of 12x^3+3x^2-4x is 48

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integral from 0 to 2 of 12x^3+3x^2-4x

\int_{0}^{2} 12 x^{3} + 3 x^{2} - 4 x d x

48

Solution steps

\int_{0}^{2} 12 x^{3} + 3 x^{2} - 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_{0}^{2} 12 x^{3} d x + \int_{0}^{2} 3 x^{2} d x - \int_{0}^{2} 4 x d x

\int_{0}^{2} 12 x^{3} d x = 48

\int_{0}^{2} 3 x^{2} d x = 8

\int_{0}^{2} 4 x d x = 8

= 48 + 8 - 8

Simplify

= 48

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What is the integral from 0 to 2 of 12x^3+3x^2-4x ?
The integral from 0 to 2 of 12x^3+3x^2-4x is 48