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- 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?

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?