What is the integral from 1 to 6 of 12x^3-9x^2+2 ?

The integral from 1 to 6 of 12x^3-9x^2+2 is 3250

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integral from 1 to 6 of 12x^3-9x^2+2

\int_{1}^{6} 12 x^{3} - 9 x^{2} + 2 d x

3250

Solution steps

\int_{1}^{6} 12 x^{3} - 9 x^{2} + 2 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}^{6} 12 x^{3} d x - \int_{1}^{6} 9 x^{2} d x + \int_{1}^{6} 2 d x

\int_{1}^{6} 12 x^{3} d x = 3885

\int_{1}^{6} 9 x^{2} d x = 645

\int_{1}^{6} 2 d x = 10

= 3885 - 645 + 10

Simplify

= 3250

\frac{d}{d x} (lo g_{2} (\frac{( 3 x + 1 )}{x ^{2} + 1}))

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\int x^{4} e^{- 3 x} d x

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7

What is the integral from 1 to 6 of 12x^3-9x^2+2 ?
The integral from 1 to 6 of 12x^3-9x^2+2 is 3250