What is the integral from-1 to 3 of (12x^3-2x+5) ?

The integral from-1 to 3 of (12x^3-2x+5) is 252

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integral from-1 to 3 of (12x^3-2x+5)

\int_{- 1}^{3} (12 x^{3} - 2 x + 5) d x

252

Solution steps

\int_{- 1}^{3} 12 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_{- 1}^{3} 12 x^{3} d x - \int_{- 1}^{3} 2 x d x + \int_{- 1}^{3} 5 d x

\int_{- 1}^{3} 12 x^{3} d x = 240

\int_{- 1}^{3} 2 x d x = 8

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

= 240 - 8 + 20

Simplify

= 252

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What is the integral from-1 to 3 of (12x^3-2x+5) ?
The integral from-1 to 3 of (12x^3-2x+5) is 252