Improper Integral Domain Question

[v0id19]

Homework Statement

I have to integrate this equation for my AP Calc BC class:
$$\int_{0}^{1}\frac{dx}{\sqrt{1-x^2}}$$

Homework Equations

I have to use the definition of an improper integral.

The Attempt at a Solution

I know that it is $$\arcsin(x)$$ from 0 to 1, and both are in the domain of the arcsin function, so i don't need to use the improper integral equation, and the answer is $$\frac{\pi}{2}$$. But I find it weird that I'd be graded on a question that i don't need to use the topic for. Am I missing anything??

 

[Mark44]

Yes. The integrand isn't defined at x = 1, which makes it an improper integral. For this reason you need to use a limit to evaluate it. I.e.,
$$\lim_{a \rightarrow 1^-} \int_0^a \frac{dx}{\sqrt{1 - x^2}}$$

 

[v0id19]

oh. so it's the domain of the integrand. thanks :D