What is the integral from 0 to 3 of (3x^2+4x-1) ?

The integral from 0 to 3 of (3x^2+4x-1) is 42

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integral from 0 to 3 of (3x^2+4x-1)

\int_{0}^{3} (3 x^{2} + 4 x - 1) d x

42

Solution steps

\int_{0}^{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_{0}^{3} 3 x^{2} d x + \int_{0}^{3} 4 x d x - \int_{0}^{3} 1 d x

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} 4 x d x = 18

\int_{0}^{3} 1 d x = 3

= 27 + 18 - 3

Simplify

= 42

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What is the integral from 0 to 3 of (3x^2+4x-1) ?
The integral from 0 to 3 of (3x^2+4x-1) is 42