Cx 2cost y 2sint Compute dxdt dydt Write integrand in term

C:x = 2cost y = 2sint Compute dx/dt, dy/dt. Write integrand in terms of t. Evaluate integral.

Solution

I = integral of (-ydx - xdy)
x = 2cost, y = 2sint
dx = -2sintdt, dy= 2costdt
putting these values above
I = integral of (-2sint*-2sintdt - 2cost*2costdt)
I = integral of (4sin^2t + 4cos^2t)dt
I = integral of 4dt........(because sin^2t+cos^2t = 1)
integrating wrt t
I = 4t
apply limit from 0 to /2
I = 2