QRAwarrior
Evaluate the definite integral from u = 0 to u = -4 of:
\sqrt{1 + u^2}
dx
As you may have noticed, I have already done U-sub.
Delete
Share
This Question is Closed
Mimi_x3
Best Response
You've already chosen the best response.
0
Then where do you needhelp with?
QRAwarrior
Best Response
You've already chosen the best response.
0
Evaluating
QRAwarrior
Best Response
You've already chosen the best response.
0
Where do you people get your bike avatars from?
QRAwarrior
Best Response
You've already chosen the best response.
0
I do not want "Google" as an answer... :O
lgbasallote
Best Response
You've already chosen the best response.
0
looks trig sub...have you learned that yet?
QRAwarrior
Best Response
You've already chosen the best response.
0
Yes
lgbasallote
Best Response
You've already chosen the best response.
0
but we really did gust google this! i swear! :(
Mimi_x3
Best Response
You've already chosen the best response.
0
What's the whole question?
lgbasallote
Best Response
You've already chosen the best response.
0
just*
lgbasallote
Best Response
You've already chosen the best response.
0
|dw:1337521244254:dw|
QRAwarrior
Best Response
You've already chosen the best response.
0
|dw:1337521266266:dw|
QRAwarrior
Best Response
You've already chosen the best response.
0
Yes I know that trig sub.
lgbasallote
Best Response
You've already chosen the best response.
0
|dw:1337521291094:dw|
QRAwarrior
Best Response
You've already chosen the best response.
0
But ultimately, you have to put a -4 into a trigonometric function's argument. How will that work?
Mimi_x3
Best Response
You've already chosen the best response.
0
the problem is subbing in the limits???
LagrangeSon678
Best Response
You've already chosen the best response.
1
convert the limits when using the trig sub
lgbasallote
Best Response
You've already chosen the best response.
0
dont forget to change back to x before evaluating
Mimi_x3
Best Response
You've already chosen the best response.
0
No, you don't need to convert back
lgbasallote
Best Response
You've already chosen the best response.
0
otherwise you'll have to convert the limits in terms of theta
QRAwarrior
Best Response
You've already chosen the best response.
0
Ok let me see what happens:
- tan(θ) = u/1
- sec(θ) = \sqrt{1 + u^2}
Then,
sec^2(θ)dθ = du
lgbasallote
Best Response
You've already chosen the best response.
0
yep.. \[\int \sec^3 \theta d\theta\]
QRAwarrior
Best Response
You've already chosen the best response.
0
Then what is limits of integration wrt θ?
QRAwarrior
Best Response
You've already chosen the best response.
0
What is arctan(-4)?
QRAwarrior
Best Response
You've already chosen the best response.
0
How did you get that?
QRAwarrior
Best Response
You've already chosen the best response.
0
I got sec^3(θ)
lgbasallote
Best Response
You've already chosen the best response.
0
it was sec^3 theta...ohh woops
lgbasallote
Best Response
You've already chosen the best response.
0
sec^3 theta = (sec^2 theta)sec theta
(1+ tan^2 theta) sec theta
\[\int \sec \theta + \tan^2 \theta \sec \theta\] lol got me stuck now
QRAwarrior
Best Response
You've already chosen the best response.
0
|dw:1337523905957:dw|
@LagrangeSon678
@shivam_bhalla
QRAwarrior
Best Response
You've already chosen the best response.
0
@experimentX
experimentX
Best Response
You've already chosen the best response.
1
evaluate it individually ..
\[ \int \sec \theta d\theta = \ln |\sec\theta + \tan\theta|\]
shivam_bhalla
Best Response
You've already chosen the best response.
1
@QRAwarrior , i just remember this
\[\int\limits_{}^{}\sqrt{x^2+a^2} = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
shivam_bhalla
Best Response
You've already chosen the best response.
1
You can go ahead and derive this
shivam_bhalla
Best Response
You've already chosen the best response.
1
I forgot the dx in the question :P
QRAwarrior
Best Response
You've already chosen the best response.
0
Ok, skrew that question and instead would you mind looking at this: You have the curves x = (y-7)^2, and x = 4 that enclose a region. You must rotate this region about y = 5.
|dw:1337525316103:dw|
I need to use the shell method here, but it looks like as if I will get two cylinders here.
Thanks for the help on the opening post question...
experimentX
Best Response
You've already chosen the best response.
1
I think that's formula for standard integral ... what do we call it ... i have bunch of them in my books ... but they are derived in the same way!!
experimentX
Best Response
You've already chosen the best response.
1
brb
shivam_bhalla
Best Response
You've already chosen the best response.
1
slight Correction:
\[\int\limits\limits_{}^{}\sqrt{x^2+a^2} \space \space dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
QRAwarrior
Best Response
You've already chosen the best response.
0
@shivam_bhalla look at my recent post above
QRAwarrior
Best Response
You've already chosen the best response.
0
Those are two functions!
QRAwarrior
Best Response
You've already chosen the best response.
0
I just realized! I would have to use the washer.
shivam_bhalla
Best Response
You've already chosen the best response.
1
@QRAwarrior , I am not so good at this. @TuringTest can surely help you in this :)
QRAwarrior
Best Response
You've already chosen the best response.
0
Alright thanks your help for the above.
QRAwarrior
Best Response
You've already chosen the best response.
0
@TuringTest help please
@amistre64
@Hero
@asnaseer
QRAwarrior
Best Response
You've already chosen the best response.
0
@FoolForMath would you mind helping me here?
QRAwarrior
Best Response
You've already chosen the best response.
0
Someone is bound to come!
QRAwarrior
Best Response
You've already chosen the best response.
0
@apoorvk help please?
QRAwarrior
Best Response
You've already chosen the best response.
0
Please look at the most recent question (it is the one with the sketch just above, NOT THE OPENING POST)