1. I keep having trouble with my trigonometric substitutions.

take for example:

integral from 0 to 1: dx / sqrt(1-x^2) (this also an improper integral)

Here's what I'm doing:

x=sin(t) dx=cos(t)

1-x^2 = cos(t)^2 <--trig identity of 1-sin^2 = cos^2

so now I have:

cos(t)/sqrt(cos(t)^2) which gives me:

cos(t)/ abs(cos(t)) = 1

however, i'm making a mistake. where?  2.

3. i think it might have something to do with inverse trigonometric functions...

...can you guys understand the way I typed the eq?  4. Originally Posted by Wilhelm
x=sin(t) dx=cos(t)
if x=sin(t) then dx/dt = cos(t), thus dx = cos(t)dt
which changes your result to be cos(t)dt/cos(t) = dt

does that help?  5. Just a question, why is cos(t)/|cos(t)| = 1? Oh and what are the new bounds for the integral?  Bookmarks
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