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

The integral from 1 to 3 of (3x^2-4x+1) is 12

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

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

12

Solution steps

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

\int_{1}^{3} 3 x^{2} d x = 26

\int_{1}^{3} 4 x d x = 16

\int_{1}^{3} 1 d x = 2

= 26 - 16 + 2

Simplify

= 12

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What is the integral from 1 to 3 of (3x^2-4x+1) ?
The integral from 1 to 3 of (3x^2-4x+1) is 12