Well now I'm not to sure. After substituting in,
x = √12*sin(u)
I got,
dx = √12*cos(u)du
Putting both of these back into the integral I then had,
∫√(12 -12*sin2(u))*√12*cos(u)du
=∫√(12(1 -sin2(u))*√12*cos(u)du
using the trig identity, cos2(u) +sin2(u) = 1
I then realized...
Well...
It would seem I have fried my brain with the late nights spent trying to work this out. So far I've got;
∫cos3u.du
and once again, I know the answer (=1/3*sin3u +sinu), but for the life of me I can't figure out how to get there. Is having the function in the form cos3u the right...
Thanks Sammy and Mark,
Will give it a go. Also, I think Mark's the first person I've encountered who's actually given a methodology for determining an appropriate substitution. Thanks :)
Regards,
Chris
Homework Statement
Integrate the function,
f(x) = √(12 -x2)
Homework Equations
n/a
The Attempt at a Solution
I tried splitting the function up as follows:
f(x) = √(12+x)*√(12-x)
then I tried substituting in,
w=12-x and dw=-dx, to get...
Thanks all for your timely replies, much appreciated and my apologies to eumyang for the misleading title. I had a sneaking suspicion that the "something-or-other" I was searching for was infact "function" and had gone through my question at the last moment prior to posting, to change "function"...
Hi,
In school (I think) I recall there being a test for an equation which determined whether or not it was a valid 'something-or-other' and it was simply that if you could draw a vertical line anywhere on the graph of the equation, that crossed the line more than once, it was not a valid...
Thanks all for the quick replies. I think Charlesmanima pretty much summed up what I was after.
Just to clarify though, are the d/dx, dx and dy terms, just symbols that cannot be manipulated by the usual mathematical methods (excluding convenient coincidences)?
Regards
Chris.
How do the "d" terms in differential equations work?
Hi,
I was hoping someone could explain how the "d" terms in differential equations work? For example,
d2y/dx2 = 4x3 +1
To solve I have been rearranging to get,
d2y = (4x3 +1)dx2
and then doing a double integral of each side...
Hi,
I was wondeing if anyone could help me out here. What form of energy can most efficiently be converted to electrical energy (by current means)?
Cris