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

The integral from 1 to 3 of (3x^2-2x+1) is 20

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

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

20

Solution steps

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

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

\int_{1}^{3} 2 x d x = 8

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

= 26 - 8 + 2

Simplify

= 20

What is the integral from 1 to 3 of (3x^2-2x+1) ?
The integral from 1 to 3 of (3x^2-2x+1) is 20