What is the integral from 2 to 4 of (x^3+6x^2+9x+1) ?

The integral from 2 to 4 of (x^3+6x^2+9x+1) is 228

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integral from 2 to 4 of (x^3+6x^2+9x+1)

\int_{2}^{4} (x^{3} + 6 x^{2} + 9 x + 1) d x

228

Solution steps

\int_{2}^{4} x^{3} + 6 x^{2} + 9 x + 1 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}^{4} x^{3} d x + \int_{2}^{4} 6 x^{2} d x + \int_{2}^{4} 9 x d x + \int_{2}^{4} 1 d x

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 6 x^{2} d x = 112

\int_{2}^{4} 9 x d x = 54

\int_{2}^{4} 1 d x = 2

= 60 + 112 + 54 + 2

Simplify

= 228

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What is the integral from 2 to 4 of (x^3+6x^2+9x+1) ?
The integral from 2 to 4 of (x^3+6x^2+9x+1) is 228