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

  • Thread starter randoreds
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  • #1
randoreds
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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..?
 

Answers and Replies

  • #2
Mentallic
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the lower bound is [itex]x=\pi/3[/itex] right? And [itex]u=\sec(x)[/itex] so the lower bound after the u-substitution will be [itex]u=\sec(\pi/3)[/itex] and similarly the upper bound will be [itex]u=\sec(0)[/itex]
 
  • #3
marvincwl
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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.
 
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  • #4
randoreds
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the lower bound is [itex]x=\pi/3[/itex] right? And [itex]u=\sec(x)[/itex] so the lower bound after the u-substitution will be [itex]u=\sec(\pi/3)[/itex] and similarly the upper bound will be [itex]u=\sec(0)[/itex]

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

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.

[tex]\sec(x)=\frac{1}{\cos(x)}[/tex]

[tex]\csc(x)=\frac{1}{\sin(x)}[/tex]

[tex]\cot(x)=\frac{1}{\tan(x)}[/tex]

So then what is [itex]\sec(\pi/3)[/itex] ?

because I have no idea when sec = pi/3 and don't really remember how to figure it out ; /
You're not looking for when "sec" = pi/3, you're looking for sec(pi/3).

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

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