Question

We had a test question that said evaluate the line integral zdx +xdy +ydx over c (c is parameterized by x=t^2 , y=t^3, z=t^2, from t=0 to 1). I took the parameterized variable, and multiplied it by its derivative, then added and evaluated, and the answer came out to be 7/5, which is apparently very wrong (4/15 for the question). What is the right way of doing this problem?

Answer 1

My work was as such \[\int\limits_{0}^{1} t^2 \sqrt{(2t^2)} dt + \int\limits_{0}^{0}t^2 \sqrt{(3t^2)} +\int\limits_{0}^{1}t^3\sqrt{(2t^2)}\]