MATH529 L20 Integration in the complex plane

Path integral

Evaluate on C: x(t)=4 cos t, y(t)=4 sin t, 0⩽t⩽π/2
(∫_C^□)x (y^2)dx

Parametric evaluation

Clear["Global`*"];

Clear[x,y]; x[t_] = 4 Cos[t]; y[t_] = 4 Sin[t];
Integrate[x[t] ((y[t])^2) D[x[t],t],{t,0,π/2}]

Explicit evaluation

Clear[x,y];Integrate[x (16-(x^2)),{x,4,0}]