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

The integral from 2 to 6 of 8x^3+3x^2+6x+3 is 2876

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

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

2876

Solution steps

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

\int_{2}^{6} 8 x^{3} d x = 2560

\int_{2}^{6} 3 x^{2} d x = 208

\int_{2}^{6} 6 x d x = 96

\int_{2}^{6} 3 d x = 12

= 2560 + 208 + 96 + 12

Simplify

= 2876

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What is the integral from 2 to 6 of 8x^3+3x^2+6x+3 ?
The integral from 2 to 6 of 8x^3+3x^2+6x+3 is 2876