What is the integral from 0 to 4 of (3x^2-2x+1) ?

The integral from 0 to 4 of (3x^2-2x+1) is 52

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integral from 0 to 4 of (3x^2-2x+1)

\int_{0}^{4} (3 x^{2} - 2 x + 1) d x

52

Solution steps

\int_{0}^{4} 3 x^{2} - 2 x + 1 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}^{4} 3 x^{2} d x - \int_{0}^{4} 2 x d x + \int_{0}^{4} 1 d x

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

\int_{0}^{4} 2 x d x = 16

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

= 64 - 16 + 4

Simplify

= 52

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What is the integral from 0 to 4 of (3x^2-2x+1) ?
The integral from 0 to 4 of (3x^2-2x+1) is 52