### Calculus help (changing limits of integration)

PostPosted:

**Wed Sep 14, 2011 5:35 pm**Amazingly, I'm actually kinda understand most of the calc I've done tonight, but this one piece of this problem is stumping me.

I have an integral from 1 to 2. I'm changing from x in the problem to sec(y) (so x = sec(y)). I know that the limits end up being from 0 to pi/3, but I can't figure out how.

I worked it out to this:

2 = sec(y) ; sec^(-1) (2) = y

1 = sec(y) ; sec^(-1) (1) = y

And sec^(-1) would be cos, right? So I have cos(2) = y and cos(1) = y but have no clue how to get to pi/3 and 0 from those.

Can anyone help me out here?

I also tried to just convert back from y to x in the end, but couldn't do that either. My end answer (before evaluating limits) is tan(y) - y, which I confirmed as being correct. But (tan(sec(2)) - 2) - (tan(sec(1)) - 1) didn't get me any closer to sqrt(3) - pi/3 (which is the final answer I'm looking for).

I have an integral from 1 to 2. I'm changing from x in the problem to sec(y) (so x = sec(y)). I know that the limits end up being from 0 to pi/3, but I can't figure out how.

I worked it out to this:

2 = sec(y) ; sec^(-1) (2) = y

1 = sec(y) ; sec^(-1) (1) = y

And sec^(-1) would be cos, right? So I have cos(2) = y and cos(1) = y but have no clue how to get to pi/3 and 0 from those.

Can anyone help me out here?

I also tried to just convert back from y to x in the end, but couldn't do that either. My end answer (before evaluating limits) is tan(y) - y, which I confirmed as being correct. But (tan(sec(2)) - 2) - (tan(sec(1)) - 1) didn't get me any closer to sqrt(3) - pi/3 (which is the final answer I'm looking for).