Question

Evaluate the line integral:
Int(x^2 dx +y^2 dy) \[\int\limits_{C}^{}x ^{2}dx+y ^{2}dy\]
C consists of the arc of the circle x^2+y^2=4 from (2,0) to (0,2) followed by the line segment from (0,2) to (4,3)

Answer 1

@phi @amistre64 @TuringTest @hartnn @Zarkon @inkyvoyd does anyone know how I would go about solving this?

Answer 2

one way is replace y and dy with functions of x. Because you have two different equations for the 2 "lines", you have two problems

for the arc of the circle, y^2= 4-x^2 and dy = -x/sqrt(4-x^2) dx
the limits are x= 2 to 0

for the line, y= x/4 +2 and dy = 1/4 dx
the limits are x= 0 to 4

Answer 3

Wouldn't you parameterize the curve of the circle, so it was(2cost,2sint)? Also parameterizing the line segment I got (4-4t,3-t), but I'm not sure where to go from there