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

The integral from 2 to 6 of (4x^3-x+2) is 1272

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

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

1272

Solution steps

\int_{2}^{6} 4 x^{3} - x + 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_{2}^{6} 4 x^{3} d x - \int_{2}^{6} x d x + \int_{2}^{6} 2 d x

\int_{2}^{6} 4 x^{3} d x = 1280

\int_{2}^{6} x d x = 16

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

= 1280 - 16 + 8

Simplify

= 1272

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What is the integral from 2 to 6 of (4x^3-x+2) ?
The integral from 2 to 6 of (4x^3-x+2) is 1272