Which Method to Use for Testing Convergence in Integrals with Substitution?

[heal]

Homework Statement

Use integration, the direct comparison test, or the limit comparison test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

Homework Equations

∫sinθdθ/√π-)

The Attempt at a Solution

I don't know which method to use and why in this case why I would apply one of them. Our instructor has not gone through in detail which methods for which cases. Thank you.
I'm guessing that the Direct Comparison Test would be useful here. Though, I am not sure what equation to use as a comparison.

 

[LCKurtz]

Homework Statement

Use integration, the direct comparison test, or the limit comparison test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

Homework Equations

∫sinθdθ/√π-)

What are the limits on the integral? What is that supposed to be after the / ?

 

[heal]

What are the limits on the integral? What is that supposed to be after the / ?

The limits are from 0 to π.

After the / it's "rad(π - θ)


Sorry.

 

[LCKurtz]

So it is$$
\int_0^\pi \frac {\sin \theta}{\sqrt{(\pi -\theta)}}\, d\theta$$

The problem is the denominator is 0 when $\theta = \pi$. Your problem is to figure out whether that makes the integral diverge or not. Of course, the numerator is 0 there too, so it could be either way. While it isn't absolutely necessary, still I would suggest the substitution $u = \pi - \theta$ to simplify it and move the difficulty to $u=0$. Then see what you think. You might find some inequality to try for comparison.