Surface area inside an elliptic cylinder

MasterWu77
Messages
21
Reaction score
0

Homework Statement



Find the surface area of that part of the plane 8x+3y+z=9 that lies inside the elliptic cylinder (x^2/64) + (y^2/9) =1

Homework Equations



not sure what equations i need to use. probably parametrization of a region

The Attempt at a Solution



i'm not quite sure how to start this problem. how do i related the elliptic cylinder with the plane?
 
Physics news on Phys.org
Hi MasterWu77! :smile:

You could just say it's a projection, and divide the base area of the cylinder by the appropriate cosine. :wink:
 
ok but how would i say that it is a projection and what exactly do you mean by the appropriate cosine?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Understanding the argument of the surface area integral
Replies
7
Views
2K
Surface of a Cylinder inside a Sphere
Replies
4
Views
2K
Surface area of a circular cylinder cut by a slanted plane
Replies
10
Views
3K
Understanding why we compute surface area as we do
Replies
1
Views
1K
Surface area bounded by 2 different planes
Replies
4
Views
1K
Surface integral: Calculate the heat flow from a cylinder
Replies
1
Views
2K
Calculating 3D Cylinder Volumes & Areas With Constants
Replies
14
Views
3K
Surface Area of Cylinder inside of sphere
Replies
1
Views
6K
How Do You Calculate the Surface Area of a Cylinder Within a Sphere?
Replies
16
Views
9K
Checking divergence theorem inside a cylinder and under a paraboloid
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top