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

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- Feb 17th 2009, 07:59 PMfruitkate21Calc 2- Integration by Trigonmetric Substitution
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 - Feb 17th 2009, 08:46 PMSoroban
Hello, fruitkate21!

If you're "really bad at this", this problem is probably fatal . . .

Quote:

. . This takes**two**subsitutions.

Let:

Substitute: .

Let:

Substitute: .

Back-substitute: .

. . and we have: .

Back-substitute: .

. . and we have: .

I'll let you evaluate it . . .

- Feb 17th 2009, 08:52 PMChris L T521
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...