Just 2 follow up questions:
1. Does sec^2=tan^2 +1 and how do we know this?
2. Is there any way to be sure what to use instead of x in trigometric substitution?
Just 2 follow up questions:
1. Does sec^2=tan^2 +1 and how do we know this?
2. Is there any way to be sure what to use instead of x in trigometric substitution?
1. Yes it does.
You should know the Pythagorean Identity
.
If you divide both sides by you find
.
2. If you prefer to use a table of integrals, then you can use the formula
.
As you can see, this result is found using trigonometric substitution.