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

The integral from-1 to 2 of (2x^4-5x^2)/(2x) is 0

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

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

0

Solution steps

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

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} \frac{2 x ^{4} - 5 x ^{2}}{2 x} d x + \int_{0}^{2} \frac{2 x ^{4} - 5 x ^{2}}{2 x} d x

\int_{- 1}^{0} \frac{2 x ^{4} - 5 x ^{2}}{2 x} d x = 1

\int_{0}^{2} \frac{2 x ^{4} - 5 x ^{2}}{2 x} d x = - 1

= 1 - 1

Simplify

= 0

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What is the integral from-1 to 2 of (2x^4-5x^2)/(2x) ?
The integral from-1 to 2 of (2x^4-5x^2)/(2x) is 0