Evaluate Trig Sub Homework: Int from Infty to -Infty

[Winzer]

Homework Statement

Having trouble evaluating:
$$\int_{\infty}^{-\infty} \frac{dz}{(z^2+x^2)^(3/2)}$$

Homework Equations

Trig sub
$$z=xtan(\theta)$$

The Attempt at a Solution

comes down to:
$$\int_{x\frac{\pi}{2}}^{-x\frac{\pi}{2}} cos(\theta) d\theta$$
goes to
$$sin(\theta)$$ from $$x\frac{\pi}{2} \longrightarrow -x\frac{\pi}{2}$$
ehh!?

 

[Gib Z]

You can change the bounds differently. Think about it, as long x is some constant, and z approaching negative infinity and positive infinity, the tan theta has to be...

 

[Winzer]

mm...just $$\frac{\pi}{2}$$

 

[rocomath]

is that supposed to be to the 3/2 power or is that a constant multiplying the denominator?

 

[Winzer]

is that supposed to be to the 3/2 power or is that a constant multiplying the denominator?

Sorry it is that quantity raised to the (3/2)

 

[Winzer]

Basically I am trying to figure out how this book got
$$\frac{z}{x^2\sqrt(z^2+x^2)}$$ with bounds from infinity to -infinity.
They then go on to get [1--1]=2.

I have to do this for a similar problem except my bounds will be L to -L.
the answer is: $$\frac{L}{x^2 \sqrt(L^2+x^2)}$$ I do not know how.
Trying to remember how to do bounds on trig subs.

 

[Winzer]

Anyone?

 

[Antineutron]

Basically I am trying to figure out how this book got
$$\frac{z}{x^2\sqrt(z^2+x^2)}$$ with bounds from infinity to -infinity.
They then go on to get [1--1]=2.

I have to do this for a similar problem except my bounds will be L to -L.
the answer is: $$\frac{L}{x^2 \sqrt(L^2+x^2)}$$ I do not know how.
Trying to remember how to do bounds on trig subs.

maybe divide top and bottom by z. then plug in the limits from infinity to -infinity

I get zero? I get (1/x^2)-(1/X^2)

 

[Gib Z]

Basically I am trying to figure out how this book got
$$\frac{z}{x^2\sqrt(z^2+x^2)}$$ with bounds from infinity to -infinity.
They then go on to get [1--1]=2.

I have to do this for a similar problem except my bounds will be L to -L.
the answer is: $$\frac{L}{x^2 \sqrt(L^2+x^2)}$$ I do not know how.
Trying to remember how to do bounds on trig subs.

Integrating with respect to z or x? State the exact question given to you please.