Vector Calculus | Part IA, 2008

Let AA be the closed planar region given by

yx2y,1yx2y.y \leqslant x \leqslant 2 y, \quad \frac{1}{y} \leqslant x \leqslant \frac{2}{y} .

(i) Evaluate by means of a suitable change of variables the integral

Axydxdy\int_{A} \frac{x}{y} d x d y

(ii) Let CC be the boundary of AA. Evaluate the line integral

Cx22ydydx\oint_{C} \frac{x^{2}}{2 y} d y-d x

by integrating along each section of the boundary.

(iii) Comment on your results.

Typos? Please submit corrections to this page on GitHub.