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I need help on the three following exercises: a) Denote by C the frontier of the triangle with vertices (0,0), (1,0) and (0,1). Show that the line integral of x⁴dx (xy) dy over C = 1/6.
b) Denote by C the circle of radius 1. Show that the line integral of -y/(x² y²) dx x/(x² y²) dy over C = 2*pi.
c) Given a,b > 0, calculate the area of x² / a² y² / b² = 1.
I'm pretty sure I know how to calculate b), but mine results in pi, not 2*pi. On a) and c), my doubts lays on how to determine the curves C on which the integral will be calculated upon.
Thanks in advance!
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