Help with a line integral please

[Helloooo]

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?

 

[pasmith]

I think you have $dy/dt$ incorrect; it should be $2a \sin t \cos t = a \sin (2t)$.

 

[Helloooo]

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!