I was hoping someone could explain to me how to do the problem
The integral from -pi/2 to 0 of cos(t)/(sqrt(1+sin^2(t)))dt
if its possible will you please show every step because i am really bad at this!!!!
Thank you
I was hoping someone could explain to me how to do the problem
The integral from -pi/2 to 0 of cos(t)/(sqrt(1+sin^2(t)))dt
if its possible will you please show every step because i am really bad at this!!!!
Thank you
Hello, fruitkate21!
If you're "really bad at this", this problem is probably fatal . . .
. . This takes two subsitutions.
Let:
Substitute: .
Let:
Substitute: .
Back-substitute: .
. . and we have: .
Back-substitute: .
. . and we have: .
I'll let you evaluate it . . .
First off, if you make the substitution , I leave it for you to show that the integral becomes
Now apply the trig substitution Thus .
Now if you know how to evaluate , then see my next paragraph. I'll assume for now you don't know how to. Note that . Now let . Thus, the integral becomes .
Since we were dealing with , we see that this is equivalent to . Thus, we have
Hopefully, you were able to follow all of this. Does it make sense?
EDIT: Soroban beat me to it...