Well its quite an easy one. The given curve is a cardioid. The limits of theta, unless otherwise mentioned is always from 0 to . The secret to finding it is that, cos=(r-4)/3 . So for any value of r in polar coordinate, (r-4)/3 will give some value. But we know cos=cos(2-), so the same value wil be given by and 2- . So if we put =2-, we get = which is maximum range for non repeatation of r values. A simpler way to find the range is: You get the minimum value of r at cos=-1, so minimum r=1. So range of r must be from 1 to 4 + 3cos. r is minimm at = and maximum of r is when cos=1 that is =0. So your can range from 0 to . However, integrating from 0 to will only give you half the area ( upper part of curve). So multiply the answer with 2 to get the full area. Solution Well its quite an easy one. The given curve is a cardioid. The limits of theta, unless otherwise mentioned is always from 0 to . The secret to finding it is that, cos=(r-4)/3 . So for any value of r in polar coordinate, (r-4)/3 will give some value. But we know cos=cos(2-), so the same value wil be given by and 2- . So if we put =2-, we get = which is maximum range for non repeatation of r values. A simpler way to find the range is: You get the minimum value of r at cos=-1, so minimum r=1. So range of r must be from 1 to 4 + 3cos. r is minimm at = and maximum of r is when cos=1 that is =0. So your can range from 0 to . However, integrating from 0 to will only give you half the area ( upper part of curve). So multiply the answer with 2 to get the full area..

1. Well its quite an easy one. The given curve is a cardioid. The limits of theta, unless otherwise
mentioned is always from 0 to . The secret to finding it is that, cos=(r-4)/3 . So for any value of r
in polar coordinate, (r-4)/3 will give some value. But we know cos=cos(2-), so the same value
wil be given by and 2- . So if we put =2-, we get = which is maximum range for non repeatation
of r values. A simpler way to find the range is:
You get the minimum value of r at cos=-1, so minimum r=1. So range of r must be from 1 to 4 +
3cos.
r is minimm at = and maximum of r is when cos=1 that is =0. So your can range from 0 to .
However, integrating from 0 to will only give you half the area ( upper part of curve). So
multiply the answer with 2 to get the full area.
Solution
Well its quite an easy one. The given curve is a cardioid. The limits of theta, unless otherwise
mentioned is always from 0 to . The secret to finding it is that, cos=(r-4)/3 . So for any value of r
in polar coordinate, (r-4)/3 will give some value. But we know cos=cos(2-), so the same value
wil be given by and 2- . So if we put =2-, we get = which is maximum range for non repeatation
of r values. A simpler way to find the range is:
You get the minimum value of r at cos=-1, so minimum r=1. So range of r must be from 1 to 4 +
3cos.
r is minimm at = and maximum of r is when cos=1 that is =0. So your can range from 0 to .
However, integrating from 0 to will only give you half the area ( upper part of curve). So
multiply the answer with 2 to get the full area.