What is the integral from 2 to 5 of (3x^2-4x+2) ?

The integral from 2 to 5 of (3x^2-4x+2) is 81

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integral from 2 to 5 of (3x^2-4x+2)

\int_{2}^{5} (3 x^{2} - 4 x + 2) d x

81

Solution steps

\int_{2}^{5} 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_{2}^{5} 3 x^{2} d x - \int_{2}^{5} 4 x d x + \int_{2}^{5} 2 d x

\int_{2}^{5} 3 x^{2} d x = 117

\int_{2}^{5} 4 x d x = 42

\int_{2}^{5} 2 d x = 6

= 117 - 42 + 6

Simplify

= 81

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What is the integral from 2 to 5 of (3x^2-4x+2) ?
The integral from 2 to 5 of (3x^2-4x+2) is 81