What is the integral from 0 to 2 of 2x^3-6x^2+4x ?

The integral from 0 to 2 of 2x^3-6x^2+4x is 0

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integral from 0 to 2 of 2x^3-6x^2+4x

\int_{0}^{2} 2 x^{3} - 6 x^{2} + 4 x d x

0

Solution steps

\int_{0}^{2} 2 x^{3} - 6 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} 2 x^{3} d x - \int_{0}^{2} 6 x^{2} d x + \int_{0}^{2} 4 x d x

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

\int_{0}^{2} 6 x^{2} d x = 16

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

= 8 - 16 + 8

Simplify

= 0

What is the integral from 0 to 2 of 2x^3-6x^2+4x ?
The integral from 0 to 2 of 2x^3-6x^2+4x is 0