Please help me solve this mathematical Problem a.) Curl b.)Green's Theorem d.) Div please pleawse?

Question

Help, please help me solve this problem , about a.)Div F b.) Curl c.) Green's Theorem ... ?

1.) F= xy^2 i + 2x^2yz j - 3yz^2 k

find: a.) Div F b.) Curl

2.) e^x cos y i + e^x sin y j

3.) ∫ F(x,y) = xy i - y^2 j

R( t ) = t^2 i + t^3

- <= t <= 1

4.) Green's theorem:

∫c x^2y dx - y^2x dy

(1,1)

(0,0)

Hope for you kind heart, i really dont know nothing about this.

please help me, i would really appreciate this kind heart of yours.

can show me the solution.

Answer 1

i am so sry i am only just going into trig. as a 9th grader sry i am not quite there yet

Answer 2

If F = Fx i + Fy j + Fz k,

then div F = delFx/delx + delFy/dely + delFz/delz

Note: Instead of del, use the symbol, which is pronounced like del. I do not know how to type it.

1)Fx = xy^2, Fy = 2x^2yz, Fz = -3yz^2

delFx/delx = y^2

delFy/dely = 2x^2z

delFz/delz = -6yz

div F = y^2 + 2x^2z - 6yz

Can you do the rest in the same way?

For curl, use the formula

(delFz/dely - delFy/delz)i + (delFx/delz - delFz/delx)j + (delFy/delx - delFx/dely)k

Do you want Div and Curl in question (2) also?

What is to be done in question (3)?

And (4) is also not clear. Green&#039;s theorem is a theorem and not a problem. So, what is to be done in (4)? Do we have to verify green&#039;s theorem? Or something else?