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

The integral from 1 to 2 of (5x^4-3x^2+2x) is 27

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

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

27

Solution steps

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

\int_{1}^{2} 5 x^{4} d x = 31

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 2 x d x = 3

= 31 - 7 + 3

Simplify

= 27

What is the integral from 1 to 2 of (5x^4-3x^2+2x) ?
The integral from 1 to 2 of (5x^4-3x^2+2x) is 27