Find the area enclose by one loop of the curve

r= 2 Cos[x] - Sec[x]

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- Jul 21st 2007, 04:29 PMcamherokidPolar Coordinate 02
Find the area enclose by one loop of the curve

r= 2 Cos[x] - Sec[x] - Jul 21st 2007, 05:30 PMJhevon
We need the limits of integration first. since the loop goes through the origin, we need to find the values of x for which the curve passes through the origin, so set r = 0

we have,

looking at the graph, we see we want the region between and

we want to go anticlockwise from to to get the desired area, but we must go from a smaller to a larger angle. so rewrite as and we are in business

So our desired area is given by

- Jul 21st 2007, 06:06 PMgalactus
That looks good, Jhevon. You could also just write it as:

Same thing. - Jul 21st 2007, 06:07 PMJhevon