Calculus question! help needed!!?

compute the work done by the force F=%26lt;2x,2y^2%26gt; along the curve C defined by C: is the quarter circle from (4,0) to (0,4).





help please! i have no idea on how to solve this!!

Calculus question! help needed!!?
You will use W=Integral(F dot dr)





by which I mean you will take the dot product of the Force vector and dr and integrate over the contour given (the quarter circle from (4.0) to (0,4)





because your path is on a circle, convert everything to polar coordinates





so, F=2x i + 2y^2 j (where i and j are unit vectors in the x and y directions) becomes





F=2 cosθ i + 2 sin^2θ j





the contour is the circle of radius 2 centered on (0,0), so:





r=2cosθ i + 2sinθ j





therefore





dr=-2sinθ dθ; i+2 cosθdθ j





so F dot dr becomes:





-4 sinθcosθdθ


+ 2 cosθsin^2θdθ





and you integrate this between the limits of θ=0


and θ=π/2