What is the integral from-8 to 2 of 1/(sqrt(|2x|)) ?

The integral from-8 to 2 of 1/(sqrt(|2x|)) is 6

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integral from-8 to 2 of 1/(sqrt(|2x|))

\int_{- 8}^{2} \frac{1}{∣ 2 x ∣} d x

6

Solution steps

\int_{- 8}^{2} \frac{1}{∣ 2 x ∣} d x

Eliminate Absolutes

= \int_{- 8}^{0} \frac{1}{- 2 x} d x + \int_{0}^{2} \frac{1}{2 x} d x

\int_{- 8}^{0} \frac{1}{- 2 x} d x = 4

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

= 4 + 2

Simplify

= 6

\frac{d}{d y} (sin (2 y))

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 0

x \to 0 lim (\frac{sin ^{5} ( x )}{x})

\frac{\partial}{\partial y} (3 x^{2} - 5 y)

y^{^{'}} = \frac{x y ^{2} - 0.5 sin ( 2 x )}{y ( 1 - x ^{2} )}

What is the integral from-8 to 2 of 1/(sqrt(|2x|)) ?
The integral from-8 to 2 of 1/(sqrt(|2x|)) is 6