Find the exact coordinates of the centroid of the lamina bounded by the curve y=1/(1+x^2), the x-axis, the y-axis, and x=1.
I got the Area to be (Pi/4)
For X-Bar, I got: (2/Pi)*ln(2)
I got stuck on the Y-Bar.
(4/Pi)*(1/2)*the integaral (1/(1+x^2)^2) dx.
This comes to (2/Pi)*the integral (1/(1+x^2)^2) dx.
I don't know how to integrate that. So can someone tell me if my area and X-Bar are correct and then help me integrate for Y-Bar?
I got B=1 in yours and D=1 in mine. It's the same thing. I'm just not getting it. I hate days like these. Nothing seems to click.
Mine: Ax^3+Bx^2+Ax+Cx+B+D = 1, A=0 from the Ax^3=0, B=0 from the Bx^2=0, C=0 from the Ax+Cx=0, and D=1 from B+D=1 and B=0
Yours: Ax^2+Bx+A+C = 1, A=0 from Ax^2=0, B=0 from Bx=0, and C=1 from A+C=1 and A=0.