Recent content by andylu224

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    Graduate Simpler Solution for Cumbersome Trig Integral?

    You've got a few errors in your integration. Integrating -2sin6x should be 1/3 cos6x and -sin12x should be 1/12 cos12x. The final answer seems alright surprisingly.
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    Series Circuit DIfferential Equation - My answer is coming out to be wrong

    First off, Your entire method could not possibly work if E(t) is not simply a constant, but thankfully in this case it is. You only made one simple mistake when you integrated di/[E-2i]. you're missing a -1/2 in front of the ln|E-2i|.
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    Find A, B with Limx->infinity Equation

    I approached the question by first factoring out x1/3 from the bracketted expression. with the remaining surdic expression, i rationalised the numerator in terms of cube roots so the numerator i would have [(x2 + x + a) - (x2 - b)] = x + a + b in it. I rearranged the x4/3 in the numerator to...
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    2 differentials, one of which is almost solved

    You did nothing wrong for the first problem. Just try plugging the terms into the original ODE again carefully. For the 2nd problem, make y' the subject and think about what happens when something is implicitly differentiated. I think the answer is ey + ex + exy = 0. Good luck.
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    Seemingly difficult complex arithmetic problem

    What's so hard about this question? It only requires some very basic trigonometric identities and properties of moduli. Several Hints: To derive T, 1) e-i(theta) = cos(theta) - i sin(theta) 2) How does one divide 2 complex numbers (ie. (x1 + iy1)/(x2 + iy2) )...
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    Solving Integral Equation: sin(x)+∫_0^π sin(x-t)y(t)dt

    i know you calculate the integral to obtain the constants, but I am just at a loss in doing what you both did. the solution to the ODE would be y = Ax + B. when inserted into the original equation, Ax + B = 1 + (int 0->1) (x-t)y(t)dt (A - (int 0->1)y(t)dt)x + (B - 1 + (int 0->1)...
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    Solving Integral Equation: sin(x)+∫_0^π sin(x-t)y(t)dt

    I'm just wondering how did get these combinations for the constants after you've plugged your solution into the integration equation.
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    Need help solving the integral: (x^2)/(2^x)

    This Integration Technique might be useful in your case: http://en.wikipedia.org/wiki/Integration_using_parametric_derivatives
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    Can an Analytic Method Solve for t in the Equation 2e^(t²) + e^t - 3e = 0?

    obviously, one solution is t = 1.
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    How do I find the volume of this?

    Use the Shell Method instead.
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    Proving Integral of (1+x^2)^n: Techniques and Examples

    I think you made a mistake typing it: It should be '+' in between the 2 fraction and the integral. Just do a simple Integration by parts without induction. Let dv=dx , u = 1/(1+x2)n In = x/(1+x2)n + 2n(integral)[x2/(1+x2)n+1]dx as 'x2 = 1 + x2 - 1', You should end up with: In =...
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    Solving 3xy^3 + (1+3x^2y^2)dy/dx=0

    You won't need to rely upon integrating factors in this case. we know dy/dx = -3xy^3/(1 + 3x^2y^2) Thus: dx/dy = -1/3xy^3 - x/y Making a simple substitution of u = xy dx/dy = (y*du/dy - u)/y^2 when the substitution is made The equation should become separable.
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    Solving 3xy^3 + (1+3x^2y^2)dy/dx=0

    For starters, it's y' + P(x)*y = q(x) For this to be true, the DE has to be linear. Do you think it is linear, separable or neither?
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    How do I evaluate the derivative of G(x) for my Calc 2 final tomorrow?

    Essentially this is using the chain rule whereby when: G(x) = (integral of f1(x) to f2(x) ) g(t) dt G'(x) = g(f2(x))*f2'(x) - g(f1(x))*f1'(x) so in your case, G'(x) = sin(-x^4)*2x - sin(-x^2)
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    Solving Complex Variables Homework

    For the second question, a big hint is to equate equivalent terms. a + bi = c + di --> a = c, b = d Don't move things across the equals sign, but work on each side separately