improper integral

[goosefraba]

Hello everyone, I need some help with the following problem:

integral 0 to 1 of 1/sqrt(1-x^2) dx

I have been letting x=sin(theta) so that I get a cos^2(theta) under the radical, but that cancels with the cos(theta) I get for dx when using trig substitution. So I end up with just the integral 0 to 1 of 1, which I don't think is right. If anybody can help with this that would be great.

Thanks

 

[Deleted member 4993]

Hello everyone, I need some help with the following problem:

integral 0 to 1 of 1/sqrt(1-x^2) dx

I have been letting x=sin(theta) so that I get a cos^2(theta) under the radical, but that cancels with the cos(theta) I get for dx when using trig substitution. So I end up with just the integral 0 to 1 of 1, which I don't think is right. If anybody can help with this that would be great.

Thanks

While substituting, you have to change the limits of integration also

x = sin(?)

when x = 0 ? ? = 0

when x = 1 ? ? = ?/2

 

[goosefraba]

Okay, well I worked it out and got an answer of pi/2...is this right?

 

[Deleted member 4993]

Okay, well I worked it out and got an answer of pi/2...is this right? <<< Should be

 

[goosefraba]

Thank you very much. I appreciate the fast responses