Recent content by Manni

The only thing I'm not sure of is if it the question is asking for solutions. If it is can I put the dy/dx equation in the standard differential form, dy/dx + P(x) = Q(x) Then, I can determine the integrating factor and solve that way. I was initially thinking of doing that, would it work?

Wait, it's dT/dt not dT/dx?

Oh I understand, thank you!

Oh, so we would integrate the constant b as a normal constant correct? I.e. b*x?

I'm a bit confused as to what I do next with this problem. Consider the initial value problem \frac{dy}{dx} = a(y-b) where y(0) = y0 With a > 0, b = 0, it represents exponential growth, while a < 0, b = 0 gives exponential decay. With y = T, a = -k, k = TA and y0=T0 it gives Newton's Law of...

I'm given the differential dy/dx = x*y*sinx / (y+1) and I need to find its solution. I apply the following steps, (y+1)/y*dy = x*sinx*dx 1 + 1/y*dy = x*sinx*dx ∫ 1 + 1/y*dy = ∫ x*sinx*dx ...skipping a few steps for convenience I get the equation y + lny = -x*cosx + sinx My problem...

LCKurtz, that's exactly what I was looking for. I apologise to the others if I the question was too ambiguous, the textbook just worded it this way. Nevertheless, thanks everyone!

I've been told this is a trick question, but I don't understand why: How would I describe the solid generated by 2∏∫ x/(1+x2)dx on [0,2] How I would do it I would rewrite the intergal as 2∏∫ x * 1/(1+x2)dx and apply substitution. I would then use the volume of disks method and integrate the...

Was just double checking if we can simplify this in the following way, ∫ sinx * √(1 + cos2x) dx = ∫ sinx * (1 + cosx) dx

Yup, I don't know why I was questioning my definition so much. Thanks Dick :)

Hey guys I was trying to think conceptually and got a little lost. If R(t) represents the rate of volume per unit time what would it's integral represent? My initial guess was that it represents the total volume over that interval of time but it feels incomplete, or even wrong. Help?

Thanks a lot, makes more sense! Forgive my ignorance by the way.

Find the length of the curve r = cos^2(theta/2) I'm hopelessly lost.

Oh, I got it! You need to sub in (A-0.300) meters for x, and not 0.300 m!

I got 3.52 m/s, and it's not even offered as one of the choices.