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

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

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

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

4

Solution steps

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

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

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

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

= 8 - 8 + 4

Simplify

= 4

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