## anonymous 5 years ago Find the center of mass of a thin plate covering the triangular region cut from the first quadrant by the line y = -x + 3, with density δ(x) = x.

1. anonymous

Take rectangular strips of length dx at a distance x from origin perpendicular to y axis dm becomes density*V. Find V in terms of x and dx(You know the equation of the line). Then integrate from 0 to 3. y coordinate is same as that of a normal triangular plate.

2. anonymous

|dw:1326959348751:dw|find side length and multiply by dx to find V

3. anonymous

ok.thanks.

4. anonymous

i wanna ask one more question to u

5. anonymous

$\int\limits_{0}^{3}$$^{?}\sqrt{9-x^2}$$x^{2}$dx

6. anonymous

err i did not get that properly do you want to integrate sqrt(9-x^2) , what is that x^2 below it?

7. anonymous

x^2.square root of 9-x^2 dx integrate this

8. anonymous

from 0 to 3

9. anonymous

put x=3cos(theta) i think just give me a minute.

10. anonymous

ok

11. anonymous

put x= 3cos t dt=-3sin t so the integral becomes -3(sin t) (3cos t)^2 sqrt(9 sin^2 t) = -81 sin^2 t cos ^2 t . sin ^2 t cos ^2 t=(sin ^2 (2t))/4.then sin ^2 (2t)=(1-cos 4t)/2 now you can integrate this easily.

12. anonymous

in the first line it was dx=-3sint dt

13. anonymous

Did you get it?

14. anonymous

thnx

15. anonymous

No problem.