- #1
cp255
- 54
- 0
If the mass per unit area of a surface is given by ρ=xy, find the mass if S is the part of the cylinder x2+z2=25 which is in the first octant and contained within the cylinder x2+y2=16.So here was my attempt.
I parametrized the curve.
x2+z2=25
r(u, v) = <5cos(u), v, 5sin(u)>
I then plugged into the bounds
x2+y2=16.
25cos2(u) + v2 = 16
v = sqrt(16 - 25cos2(u))
Next I took the cross product of ru X rv. Its magnitude is a constant 5.
Now I solved the integral with bounds 0 < u < Pi/2 and 0 < v < sqrt(16 - 25cos2(u))
∫∫25 v cos(u) du dv
This returns the result of -25/3 but since we are looking for a mass I submitted the answer of positive 25/3 and this is wrong. I checked the integration on my calculator and it gets the same result.
I parametrized the curve.
x2+z2=25
r(u, v) = <5cos(u), v, 5sin(u)>
I then plugged into the bounds
x2+y2=16.
25cos2(u) + v2 = 16
v = sqrt(16 - 25cos2(u))
Next I took the cross product of ru X rv. Its magnitude is a constant 5.
Now I solved the integral with bounds 0 < u < Pi/2 and 0 < v < sqrt(16 - 25cos2(u))
∫∫25 v cos(u) du dv
This returns the result of -25/3 but since we are looking for a mass I submitted the answer of positive 25/3 and this is wrong. I checked the integration on my calculator and it gets the same result.