How Do You Calculate Line Integrals and Center of Mass for Complex Shapes?

[hytuoc]

1) Integral of bound C of function x*e^y ds; C is the line segment from (-1,2) to (1,1).
How do i get the bound and the x and y in parameter form?
Show me please! I need to learn!
2)A wire w/ constante density has the sahpe of the helix x=a*cos(t), y=a*sin(t), z=bt, 0<=t<=3 pi. Find its mass a center of mass
For this one, is the function = k, for which k is any constant? and then do the integral from 0 to 3 pi??

**mass = integral from 0 to 3 pi, of k*sqrt[ -a^2*sin^2(t) +a^2*cos^2(t)+b^2] dt ??
Thanks so much

 

[dextercioby]

For the second,you may want to check again the differentiation.The integral is very simple...

Daniel.

 

[Galileo]

There are many ways of getting an upper bound of xe^y on the line segment.
Since on this segment |x|\leq 1 and e^y \leq e^2 we have |xe^y|\leq e^2.

Not sure if this was what you were looking for.