Math Is Fun Forum

almost there

Member

Registered: 2009-11-11

Posts: 21

integration by substitution

I have not done calculus in years but am in a course that requires me to try and recall my calculus...I'm not doing so hot.

Integrate

using the substitution

.

I remember that I cannot simply stick "tan(y)" in for "x", but I also have to find an expression to substitute-in for "dx".

How do I find this expression that will take the place of "dx"? Do I do

? If not, what is the appropriate method? And if so, please let me know--a little confirmation never hurt.

Thanks in advance.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: integration by substitution

Yeah that substitution and expression for dx are correct, but you have to do a bit of algebra before you can get everything in terms of y.
After you sub in x = tan(y), apply a trig identity so that your expression turns into something more usable

almost there

Member

Registered: 2009-11-11

Posts: 21

Re: integration by substitution

Yea, it made intuitive sense, and I figured (after my post) that my method was correct when I evaluated the integral. Thank you for your confirmation of that as well as for your inclusion of the evaluation of the integral afterward (it was great to compare my work to someone else's)!

Yeah that substitution and expression for dx are correct, but you have to do a bit of algebra before you can get everything in terms of y.
After you sub in x = tan(y), apply a trig identity so that your expression turns into something more usable