What is the integral from 1 to 3 of (3x^2-5x+2) ?

The integral from 1 to 3 of (3x^2-5x+2) is 10

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integral from 1 to 3 of (3x^2-5x+2)

\int_{1}^{3} (3 x^{2} - 5 x + 2) d x

10

Solution steps

\int_{1}^{3} 3 x^{2} - 5 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_{1}^{3} 3 x^{2} d x - \int_{1}^{3} 5 x d x + \int_{1}^{3} 2 d x

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

\int_{1}^{3} 5 x d x = 20

\int_{1}^{3} 2 d x = 4

= 26 - 20 + 4

Simplify

= 10

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

\int_{1}^{2} g (x) d x

\int_{0}^{2} (12 - t) t d t

\int_{1}^{10} 3 x d x

\int_{2}^{6} 16 - 2 x d x

What is the integral from 1 to 3 of (3x^2-5x+2) ?
The integral from 1 to 3 of (3x^2-5x+2) is 10