Question

Line Integral help please!

r=(5costsint)i+(5sin^2t)j+(5cost)k

this curve lies on a sphere with equation x^2+y^2+z^2=25

Evaluate the c integral z ds using this curve.

I will write more exact below.

Answer 1

Evaluate \[\int\limits_{c}^{} z ds\] for curve above.

Answer 2

t from where to where.

Answer 3

I think 0 to 2pi because its a sphere?

Answer 4

well first

x^2+y^2+z^2=25

Solve for z

take z and replace x by 5costsint, y by 5sin^2sin and k by 5cost
Basically plug into x,y, and z the i,j ant components this gives z(t) (z with respect to t)

then

take tha magninuted of vector | r | I assume you know how to do that



then take that magnitude and multiply by z(t): |r|*z(t)


Finally integrate wrt: intigrate (|r|*z(t)*dt)


You assume from 0 to 2pi

Answer 5

\[
|r| =5\\
\int_0^{2 \pi} 5 ( 5 \cos(t)) dt=0
\]