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Posted: 4/6/2006 3:54:54 PM EDT
it is a double integration problem:


integrate (from 0 to 1) the integral (from 0 to x^(1/2)) {15x-4y} dydx


help me.
Link Posted: 4/6/2006 4:16:02 PM EDT
is it going to happen?
Link Posted: 4/6/2006 4:18:14 PM EDT
[Last Edit: 4/6/2006 4:18:47 PM EDT by capnrob97]
Sorry, took Calc I, II, III in college over 20 years ago, haven't used it since.
Link Posted: 4/6/2006 4:24:48 PM EDT
calc was 15 years ago man, good luck

txl
Link Posted: 4/6/2006 4:32:54 PM EDT

Originally Posted By mtechgunman:
it is a double integration problem:


integrate (from 0 to 1) the integral (from 0 to x^(1/2)) {15x-4y} dydx


help me.



This is why I drink while on the boards..
Link Posted: 4/6/2006 4:35:50 PM EDT
Last calc class Fall semester 1971... Yeah I'll be right on that one...
Link Posted: 4/6/2006 4:40:37 PM EDT
Link Posted: 4/6/2006 4:46:00 PM EDT
The answer as given by my TI-89 Titanium is...

five.

That is, if you were asking:
Link Posted: 4/6/2006 4:50:12 PM EDT
I am too drunk to tackle this one, and I really don't use double integrals that much.

Link Posted: 4/6/2006 4:50:15 PM EDT

Originally Posted By MagKnightX:
The answer as given by my TI-89 Titanium is...

five.

That is, if you were asking:
img.photobucket.com/albums/v413/MagKnightX/int1.gif



badass, thats what i got.

ar15.com comes through again!
Link Posted: 4/6/2006 4:51:50 PM EDT
Get yourself a TI-89. They're indispensable for calculus.
Link Posted: 4/6/2006 4:53:28 PM EDT
The answer is 5.

First integrate with respect to dy.

You get

15XY - 2Y^2 dx | 0 to x^2

Next, plug in 0 and x^2 whereever you see a Y

You get:

15(X)(X^1/2) - 2(x^1/2)^2 dx

Simplify:

15X^3/2 - 2X dx

Now integrate again with respect to X, you GET:

(15/2.5)(X^5/2) - X^2 evaluated at 0 to 1

Plug in the 1 and you get:

6 - 1 = 5

Your welcome.

-Fidel
Link Posted: 4/6/2006 4:54:30 PM EDT
Damnit too late, but at least I was right.

Link Posted: 4/6/2006 4:57:07 PM EDT
one more question:

what is the graph of 4x + y^2 - 4z^2 called? (the name of the shape)
Link Posted: 4/6/2006 4:57:42 PM EDT

Originally Posted By MagKnightX:
Get yourself a TI-89. They're indispensable for calculus.



there is one sitting in front of me.
Link Posted: 4/6/2006 4:58:57 PM EDT

Originally Posted By Fidel:
Damnit too late, but at least I was right.




Good job!
Link Posted: 4/6/2006 4:59:12 PM EDT
[Last Edit: 4/6/2006 5:12:12 PM EDT by MagKnightX]

Originally Posted By mtechgunman:
one more question:

what is the graph of 4x + y^2 - 4z^2 called? (the name of the shape)



4x +y^2 -4z^2

is equivalent to

((4x+y^2)/4)^(1/2) = z

So let me graph it here...

Edit: looks like a curved plane with some chunks taken out of it.

I'd get a screencap, but I'm having trouble getting my comp to recognize my calc, so just graph

((4x+y^2)/4)^(1/2)

in 3d graphing mode (go to Mode > Graph > 3D and hit enter twice).

Edit: got it.





Link Posted: 4/6/2006 5:03:03 PM EDT
[Last Edit: 4/6/2006 5:06:11 PM EDT by DrCaligari1]

Originally Posted By MagKnightX:
The answer as given by my TI-89 Titanium is...

five.

That is, if you were asking:
img.photobucket.com/albums/v413/MagKnightX/int1.gif





I get:

First integrate the central integral, Which comes out to 15xy-2y^2. Evaluate this from y=0 to y=x^1/2. This gives 15x^(3/2)-2x. Now integrate this with respect to x, getting 6x^(5/2)-x^2. Evaluate this from zero to one and get 5.
Link Posted: 4/6/2006 5:06:45 PM EDT

Originally Posted By DrCaligari1:

Originally Posted By MagKnightX:
The answer as given by my TI-89 Titanium is...

five.

That is, if you were asking:
img.photobucket.com/albums/v413/MagKnightX/int1.gif





I get:

First integrate the central integral, Which comes out to 15xy+2y^2. Evaluate this from y=0 to y=x^1/2. This gives 15x^(3/2)+2x. Now integrate this with respect to x, getting 6x^(5/2)+x^2. Evaluate this from zero to one and get 7.



it would work this way, but you have to reverse the bounds. that is the hard part, everything else is simple.
Link Posted: 4/6/2006 5:15:47 PM EDT

Originally Posted By mtechgunman:
one more question:

what is the graph of 4x + y^2 - 4z^2 called? (the name of the shape)




Are you shure its not 4x^2? That would make it a hyperboloid of 1 sheet, which is a well-known shape for calc 3 students.
Link Posted: 4/6/2006 5:26:11 PM EDT
I learned multivariable calculus in Calc 4. How have you gone through three semesters of calculus without getting a calculus solving calculator or software?
Link Posted: 4/6/2006 5:34:10 PM EDT

Originally Posted By capnrob97:
Sorry, took Calc I, II, III in college over 20 years ago, haven't used it since.



Me too Calc I, II, II and Diffi Q 18 years ago and I can't remember much of it.

Link Posted: 4/6/2006 5:36:48 PM EDT
[Last Edit: 4/6/2006 5:58:44 PM EDT by mjw]

Originally Posted By mtechgunman:
one more question:

what is the graph of 4x + y^2 - 4z^2 called? (the name of the shape)




wrt your first question, I too came up with 5 as the answer, fwiw.

(eta... I corrected an oops that I had for an exponent in what follows)

Now, this question... assuming an equation, and taking 4x to the other side, and various other algebraic hocus pocus you end up with (-1/4)y^2 + z^2 = x. (Ok, it's been a while since I've taken on any Calc III problems, so I resorted to a CRC to refresh my memory). I believe this is going to generate a hyperbolic paraboloid that is saddled over the z axis, with the max/min point located at the origin and the +x axis sitting in the saddle.

I just reading back through my description...

I do not at the moment have access to Maple or I'd try to slap together something to better illustrate. Hope that helps.... heck, I hope it's right. lol
Link Posted: 4/6/2006 5:42:39 PM EDT

Originally Posted By darealickt:
I learned multivariable calculus in Calc 4. How have you gone through three semesters of calculus without getting a calculus solving calculator or software?




i like my pencil and my paper.
Link Posted: 4/6/2006 5:48:03 PM EDT
i am taking multivariable calc right now..... and failing it.

i've never failed a class before, i'm in serious trouble....
Link Posted: 4/6/2006 5:56:19 PM EDT

Originally Posted By darealickt:
I learned multivariable calculus in Calc 4. How have you gone through three semesters of calculus without getting a calculus solving calculator or software?



When I studied Calculus, we did a 5-5-3 semester hour scheme, and III was multivariable. It wasn't that many years ago..
...........
...........
Yes it was. I am in denial. Anyway, we weren't allowed the use of calculators. We were allowed to use the CRC math tables in III, however. My professor (had the same prof for I, II, III and DE) always had this at the top of every quiz and test...

LRIEF (to keep people from giving him grief about the calculator issue.. and to possibly catch someone using on during an examination), SAWFCC, SR --- Leave results in exact form, show all work for complete credit and simplify results.

He was kind of hard core I suppose, but I think probably one of the best professors I ever studied under.

Back then, I'm not sure there were any TI graphic calculators available. Maybe the TI 81. We had HPs, by gosh. I've fondled many a calculator over the years, but I still love HPs.

Anyway.... I'll shut up with my flashback. As y'all were.
Link Posted: 4/6/2006 6:01:00 PM EDT

Originally Posted By mtechgunman:
i like my pencil and my paper.




That's pretty damn refreshing. Cool avatar, btw. Since 1822...
Link Posted: 4/6/2006 6:14:13 PM EDT
[Last Edit: 4/6/2006 6:14:39 PM EDT by mtechgunman]

Originally Posted By mjw:

Originally Posted By mtechgunman:
i like my pencil and my paper.




That's pretty damn refreshing. Cool avatar, btw. Since 1822...




if you can do it on paper, you know exactly what is happening. i like to see what is going on.
i hardly ever use a calculator (for calculus, at least)
Link Posted: 4/6/2006 6:16:25 PM EDT

Originally Posted By DrCaligari1:

Originally Posted By mtechgunman:
one more question:

what is the graph of 4x + y^2 - 4z^2 called? (the name of the shape)




Are you shure its not 4x^2? That would make it a hyperboloid of 1 sheet, which is a well-known shape for calc 3 students.



That generates this:



(it looks like it's flipping back and forth, but it's actually rotating 360deg)
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