Quick question. How do you change the bounds of integration if using sec?

1. Sep 27, 2012

randoreds

And in general, always been bad at it.

If original bounds are ∫pi/3 to 0 and im changing the bounds because I'm U-substituting.
My subtitution is u=secx

so is it when cos = pi/3 and 0 or am I wrong?
so the new bound would be from pi/2 to pi/3..?

2. Sep 27, 2012

Mentallic

the lower bound is $x=\pi/3$ right? And $u=\sec(x)$ so the lower bound after the u-substitution will be $u=\sec(\pi/3)$ and similarly the upper bound will be $u=\sec(0)$

3. Sep 27, 2012

marvincwl

just plug in the limits to the substitutition.

but usually you do not substitute a sec function, usually you would substitute a simpler function.

gd luck.

Last edited: Sep 27, 2012
4. Sep 27, 2012

randoreds

No the upper bound is pi/3 the lower bound is zero(the number on the bottom of the integral sign is zero). the equation is ∫ dx/ (x^2 times sqrt(4-x^2))
So you would have to use trig and U substitution( I think)

with trig sub I got 1/4 ∫csc^2theta

so you gotta change the bounds. Before you plug anything in.
u = sec(pi/3) My question was more how do I know what that is. because you can easily find sin, cos with unit circle. but I'm confused how to do it with sec and csc.

because I have no idea when sec = pi/3 and don't really remember how to figure it out ; /

because once you change the limits you can just integrate it. which would lead to -1/4 cot

then you could just plug in those values and find the answer

5. Sep 27, 2012

Mentallic

So with that problem, what did you make your U-sub?

$$\sec(x)=\frac{1}{\cos(x)}$$

$$\csc(x)=\frac{1}{\sin(x)}$$

$$\cot(x)=\frac{1}{\tan(x)}$$

So then what is $\sec(\pi/3)$ ?

You're not looking for when "sec" = pi/3, you're looking for sec(pi/3).

So you were fine with finding specific values of cot(x)?