What is the integral from 1 to 3 of (3x^2+5x-4) ?

The integral from 1 to 3 of (3x^2+5x-4) is 38

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integral from 1 to 3 of (3x^2+5x-4)

\int_{1}^{3} (3 x^{2} + 5 x - 4) d x

38

Solution steps

\int_{1}^{3} 3 x^{2} + 5 x - 4 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} 4 d x

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

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

\int_{1}^{3} 4 d x = 8

= 26 + 20 - 8

Simplify

= 38

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What is the integral from 1 to 3 of (3x^2+5x-4) ?
The integral from 1 to 3 of (3x^2+5x-4) is 38