Help with a line integral please

Helloooo
Messages
6
Reaction score
0
Homework Statement
Show that the curve C given by
r=(a*cost*sint)i+(a*sin^2(t))j+(a*cos(t))k
, (0≤t≤pi/2)
lies on a sphere centred at the origin.
Find ∫zds of C
Relevant Equations
∫ds=∫F(r(t))·r'(t)dt
∫zds=∫acos(t)*( (acos(2t))^2+(2asin(t))^2+(-asin(t))^2 )^1/2 dt , (0≤t≤pi/2)
Simplified :
∫a^2cos(t)*(cos^2(2t)+5sin^2(t) )^1/2 dt , (0≤t≤pi/2)
However here i get stuck and i can´t find a way to rewrite it better or to integrate as it is.
Can i please get some help in this?
 
Physics news on Phys.org
I think you have dy/dt incorrect; it should be 2a \sin t \cos t = a \sin (2t).
 
pasmith said:
I think you have dy/dt incorrect; it should be 2a \sin t \cos t = a \sin (2t).
Oh okay!
I manged to solve the integration with the change and with the substitution u=sin(t)
Thank you!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top