What is the integral from 0 to 1 of 12x^2-12x^3 ?

The integral from 0 to 1 of 12x^2-12x^3 is 1

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integral from 0 to 1 of 12x^2-12x^3

\int_{0}^{1} 12 x^{2} - 12 x^{3} d x

1

Solution steps

\int_{0}^{1} 12 x^{2} - 12 x^{3} 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}^{1} 12 x^{2} d x - \int_{0}^{1} 12 x^{3} d x

\int_{0}^{1} 12 x^{2} d x = 4

\int_{0}^{1} 12 x^{3} d x = 3

= 4 - 3

Simplify

= 1

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What is the integral from 0 to 1 of 12x^2-12x^3 ?
The integral from 0 to 1 of 12x^2-12x^3 is 1