What is the integral from-1 to 2 of 2x^3-8x^2+2x+12 ?

The integral from-1 to 2 of 2x^3-8x^2+2x+12 is 45/2

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integral from-1 to 2 of 2x^3-8x^2+2x+12

\int_{- 1}^{2} 2 x^{3} - 8 x^{2} + 2 x + 12 d x

\frac{45}{2}

Decimal Notation

22.5

Solution steps

\int_{- 1}^{2} 2 x^{3} - 8 x^{2} + 2 x + 12 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}^{2} 2 x^{3} d x - \int_{- 1}^{2} 8 x^{2} d x + \int_{- 1}^{2} 2 x d x + \int_{- 1}^{2} 12 d x

\int_{- 1}^{2} 2 x^{3} d x = \frac{15}{2}

\int_{- 1}^{2} 8 x^{2} d x = 24

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

\int_{- 1}^{2} 12 d x = 36

= \frac{15}{2} - 24 + 3 + 36

Simplify

\frac{15}{2} - 24 + 3 + 36 : \frac{45}{2}

= \frac{45}{2}

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What is the integral from-1 to 2 of 2x^3-8x^2+2x+12 ?
The integral from-1 to 2 of 2x^3-8x^2+2x+12 is 45/2