Recent content by octowilli

I had another look and figured it out. I guess when I did this in terms of y my x and y coordinates got flipped. The values of the integral are correct, but the coordinates are backwards, so the centroid is at\left(\frac{584}{135},\frac{496}{189}\right)

Thank you for responding, HallsofIvy! I think I'm still confused. I thought this was the region I needed to find the centroid of: Which has an area A = \int^2_0 x^3 dx + \int^{10}_2 (10-x) dx = 36

Homework Statement Find the centroid of the region bounded by the given curves. y = x^3x + y = 10y = 0 Homework Equations \bar x = \frac{1}{A}\int^b_a xf(x) dx\bar y = \frac{1}{A}\int^b_a \frac{1}{2}(f(x))^2 dx Where A is the area of the region containing the centroid. The...

Haha, well, it was fun to do it the long way too! Thanks for helping Dick!

Alright I thought about this again. For the integral to be a rational function, the coefficients on the logs need to equal zero. so \int \frac{ax^2+bx+c}{x^2(x+1)^3} = A\cdot ln|x| - \frac{B}{x} + C\cdot ln|x+1| - \frac{D}{x+1} - \frac{E}{2(x+1)^2} simplifies to, given B = 1 above, =...

Another thought. When x = 0 in the quadratic, a(0)^2 + b(0) + c = A(0)(0+1)^3 + B(0+1)^3 + C(0^2)(0+1)^2 + D(0^2)(0+1) + E(0^2) simplifies to c = B = 1 I'm not sure what that tells me. I'll think about it.

I don't know. I messed around with this a bit more and here's what I have. \frac{ax^2+bx+c}{x^2(x+1)^3} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{(x+1)} + \frac{D}{(x+1)^2} + \frac{E}{(x+1)^3} ax^2 + bx + c = A(x)(x+1)^3 + B(x+1)^3 + C(x^2)(x+1)^2 + D(x^2)(x+1) + E(x^2) From there, using...

Homework Statement If f is a quadratic function such that f(0) = 1 and \int \frac{f(x)}{x^2(x+1)^3}dx is a rational function, find the value of f '(0). Homework Equations The Attempt at a Solution This question is presented in the context of learning about integration by...

Thanks for responding gash789! I guess I was confused by the way the axes are rotated. Looking at it again, the 2.82 N vector certainly doesn't have an x-component. Or maybe you'd like to say the x-component is 0. Anyway, let me take another shot at a_x.From the given diagram, the x-component...

Hi all, first post here! Homework Statement Find the x component of acceleration. Find the y component of acceleration. The mass of the particle is 2kg. Homework Equations The Attempt at a Solution I've only tried to find a_x. I thought that for finding component values you need to add...