What is the solution to Problem 88?

[xdrgnh]

Homework Statement

http://books.google.com/books?id=gR.... .Find the area of the shaded region&f=false Problem 88

Homework Equations

equation of each circle (x-2)^2+y^2=9
(x+2)^2+y^2=9

The Attempt at a Solution

I solve for y for the circle (x-2)^2+y^2=9 then I took the integral of that from -1 to 0. I noticed that the shape looked symmetrical so I multiplied it by 4. But when I do it algebraically and using geometry I get a different answer then when I use the calculus.

 

[Dick]

Nobody can say why you are getting different answers until you show how you did it and what you got.

 

[xdrgnh]

Nobody can say why you are getting different answers until you show how you did it and what you got.

Well I really didn't do it algebraically the internet told me how to do it algebraically and it wasn't the same answer I got with my calculus. So the integral of one of the circles is .5(9arcsin(x-2)/3)+(x-2)(9-(x-2)^2)^.5) the limits are from -1 to 0. So I evaluated it and I got 1.584, something around there. And you see the shape is symmetrical on the link I put in. So I mult it by 4 but that did not give the right answer according to the internet. Did I do it the right way.

 

[Dick]

I get something about like that for one fourth of the region. 1.548. I think you are probably right. What's the 'internets' answer?

 

[xdrgnh]

I get something about like that for one fourth of the region. 1.548. I think you are probably right. What's the 'internets' answer?

http://www.analyzemath.com/Geometry/circles_problems.html When I plug in for my radius of 3 I get 11.05

 

[Dick]

http://www.analyzemath.com/Geometry/circles_problems.html When I plug in for my radius of 3 I get 11.05

Ok, so what did you put in for the angle? It's likely not the same as in that problem.

 

[xdrgnh]

Ok, so what did you put in for the angle? It's likely not the same as in that problem.

I just did the same thing they did except using a my radius of 3 instead of 10. Do you think that my answer is right and maybe what they are doing just doesn't apply in my case. The problem is supposed to be solved using calculus not geometry.

 

[Dick]

Yes, I think your answer is right. And this problem does apply, but you have to change the angle as well, not just radius. If you actually work that example fully through you should get the same answer. In the future, could you state the question more fully before you post, instead of having us guess what your references are?

 

[xdrgnh]

Yes, I think your answer is right. And this problem does apply, but you have to change the angle as well, not just radius. If you actually work that example fully through you should get the same answer. In the future, could you state the question more fully before you post, instead of having us guess what your references are?

I posted a link which should of taken you to the question

 

[Dick]

I posted a link which should of taken you to the question

It did. But knowing the question wasn't helping to know what you were doing wrong. Which was your actual question.