# Search results

1. ### Greens Theorem

The Integral I is defined by I = Integral F . dr Where F = (x-y, xy) << This is a verticle vector, i just didn'nt know how to write it with latex. And C is a triangle with the vertices (0,0), (1,0) and (1,3) tracked anticlockwise. Calculate the line integral using greens...
2. ### Vector calculus

Homework Statement A force is applied to a particle, defined by: F(x,y)= (y^2, 2xy) << This is a verticle bracket with the y^2 ontop of the 2xy The path of the particle is straight. The particle moves from (-1,2) to (1,3) i) Calculate the work that the force F does as the...
3. ### Vector calculus

Im afraid my use of LaTeX code, sucks. My apologies to anyone friendly enough to help! The problem: A string takes a path shown by the equation below: r(t)=(t,3t^2,6t^3) Where the RHS is a verticle vector (didnt know how to code this!) and 0 <= t <= 1 The mass per unit length...
4. ### Find all critical and stationary points: Legrange multipliers

Find all critical and stationary points of the function f(x,y)=x^3-y^2 subject to the inequality constraint c(x,y)=1-x^2-y^2 >=0 So far ive deduced that I need to use a lagrange multiplier L say, so i think i need to solve the equations : 3x^2=-2Lx -2y^2=-2Ly and 1-x^2-y^2 >=0 Is...
5. ### Reversing the order of integration

Hi Im trying to evaluate a line integral, and i need to reverse the order of integration, i'll call the function f(x) as it doesnt matter too much. and the bounds are: double integral f(x) dxdy where inner integral is from x=y^2/a to x=y and the outer integral is from y=0 to y=a (where a is a...