Find the area of region A in Figure 6. F: r = 20 cosθ, rg =...

Transcript

00:01 So, here we have been given the two circles having the radius and that are meeting to each other something like this that i am drawing here.

00:13 So, for this circle the radius is r is equals to 18 cosine of theta and for this circle the radius we have been given 8 this is y axis this is the x axis.

00:26 So, we have to find the area bounded by these two regions.

00:29 So, first of all the intersection of the curves that we want to going to find out and for that we have to equate this r is equals to 8 and r is equals to 18 cosine of theta because both are belonging to the radius r and hence we get 18 cosine of theta is equals to 8.

00:52 So, cosine of theta would be equals to 8 by 10 that means 4 by 9 right from here theta would become equals to cosine inverse of 4 by 9.

01:04 So, curve areas is symmetric about what this x axis and that is why we will try to find out the area about the symmetry to x axis.

01:15 So, this can be equals to.

01:16 So, basically we have to take the two times of the area bounded by the region that is one half integration of r square d theta.

01:26 Okay that means i am taking the area of this arc because it is nothing but forming what then arc right.

01:34 So, this two two get cancel out and hence we want to going to find out the integration of the arc that is r square of d theta.

01:43 Now let us fit the limits and required value of r here.

01:49 So, this can be equals to integration over now what will be the limit we have to find this with respect to theta...

Question

Find the area of region A in Figure 6. F: $r = 20 \cos \theta$, $r_g = 8$, G: $r = 8$ $r_f = 10$

Question

Find the area of region A in Figure 6. F: $r = 20 \cos \theta$, $r_g = 8$, G: $r = 8$ $r_f = 10$

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