Recent content by Chrisistaken

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    Integrating the function √(12 -x^2)

    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...
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    Integrating the function √(12 -x^2)

    OK, Well now I'm trying to use the trig identity cos3x = 4cos3x -3cosx Sound like the right way to go? Regards, Chris
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    Integrating the function √(12 -x^2)

    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...
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    Integrating the function √(12 -x^2)

    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
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    Integrating the function √(12 -x^2)

    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...
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    High School Functions having more than one y value for a given x value

    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"...
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    High School Functions having more than one y value for a given x value

    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...
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    Undergrad How do the d terms in differential equations work?

    So for a fail safe method of working with derivatives, you would need to go back to the limit?
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    Undergrad How do the d terms in differential equations work?

    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.
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    Undergrad How do the d terms in differential equations work?

    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...
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    High School What Form of Energy Converts Most Efficiently to Electrical Energy?

    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