What is the integral from 1 to 4 of 4x^3+5x^4+2 ?

The integral from 1 to 4 of 4x^3+5x^4+2 is 1284

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integral from 1 to 4 of 4x^3+5x^4+2

\int_{1}^{4} 4 x^{3} + 5 x^{4} + 2 d x

1284

Solution steps

\int_{1}^{4} 4 x^{3} + 5 x^{4} + 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}^{4} 4 x^{3} d x + \int_{1}^{4} 5 x^{4} d x + \int_{1}^{4} 2 d x

\int_{1}^{4} 4 x^{3} d x = 255

\int_{1}^{4} 5 x^{4} d x = 1023

\int_{1}^{4} 2 d x = 6

= 255 + 1023 + 6

Simplify

= 1284

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What is the integral from 1 to 4 of 4x^3+5x^4+2 ?
The integral from 1 to 4 of 4x^3+5x^4+2 is 1284