What is the integral from 3 to 2 of (8x^3+3x^2+6) ?

The integral from 3 to 2 of (8x^3+3x^2+6) is -155

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integral from 3 to 2 of (8x^3+3x^2+6)

\int_{3}^{2} (8 x^{3} + 3 x^{2} + 6) d x

- 155

Solution steps

\int_{3}^{2} 8 x^{3} + 3 x^{2} + 6 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{2}^{3} 8 x^{3} + 3 x^{2} + 6 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_{2}^{3} 8 x^{3} d x + \int_{2}^{3} 3 x^{2} d x + \int_{2}^{3} 6 d x)

\int_{2}^{3} 8 x^{3} d x = 130

\int_{2}^{3} 3 x^{2} d x = 19

\int_{2}^{3} 6 d x = 6

= - (130 + 19 + 6)

Simplify

= - 155

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What is the integral from 3 to 2 of (8x^3+3x^2+6) ?
The integral from 3 to 2 of (8x^3+3x^2+6) is -155