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## Homework Statement

Suppose 0<a<1.

1) Show that

0<Integral(0 to a)1/(sqrt(1-x^2)<=Integral(0 to a)1/(sqrt(1-x)<=2

2) Show that I(a)=Integral(0 to a)1/(sqrt(1-x^2) is increasing and bounded by 2.

3) Deduce that Integral(0 to 1)1/(sqrt(1-x^2) exists and has an improper integral.

## Homework Equations

Not sure that there are any relevant equations that are too useful.

## The Attempt at a Solution

I can prove with simple algebra that Integral(0 to a)1/(sqrt(1-x^2)<=Integral(0 to a)1/(sqrt(1-x). But I'm not sure how to show that it is all less then 2. I don't have an atttempt for parts 2 and 3 because they heavily rely on step 1.