What is the integral from 0 to 2 of (3x^3-2x+5) ?

The integral from 0 to 2 of (3x^3-2x+5) is 18

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integral from 0 to 2 of (3x^3-2x+5)

\int_{0}^{2} (3 x^{3} - 2 x + 5) d x

18

Solution steps

\int_{0}^{2} 3 x^{3} - 2 x + 5 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}^{2} 3 x^{3} d x - \int_{0}^{2} 2 x d x + \int_{0}^{2} 5 d x

\int_{0}^{2} 3 x^{3} d x = 12

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} 5 d x = 10

= 12 - 4 + 10

Simplify

= 18

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What is the integral from 0 to 2 of (3x^3-2x+5) ?
The integral from 0 to 2 of (3x^3-2x+5) is 18