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

The integral from 2 to 4 of (1/2 x^3-3x+2) is 16

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

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

16

Solution steps

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

\int_{2}^{4} \frac{1}{2} x^{3} d x = 30

\int_{2}^{4} 3 x d x = 18

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

= 30 - 18 + 4

Simplify

= 16

What is the integral from 2 to 4 of (1/2 x^3-3x+2) ?
The integral from 2 to 4 of (1/2 x^3-3x+2) is 16