Surface area with polar coordinates, Mathematics

Assignment Help:

Surface Area with Polar Coordinates

We will be searching for at surface area in polar coordinates in this part.  Note though that all we're going to do is illustrate the formulas for the surface area as most of these integrals tend to be quite difficult.

 We want to locate the surface area of the region found through rotating,

r = f (θ)

α < θ < β

about the x or y-axis.

Like we did in the tangent and arc length sections we will write the curve in terms of a set of parametric equations.

x= r cosθ

= f (θ) cos θ

y = r sin θ

= f (θ) sin θ

If we now make use of the parametric formula for finding the surface area we'll obtain,

S = ∫ 2Πy ds                             rotation about x-axis

S = ∫ 2Πx ds                             rotation about y-axis

Where

ds = √r2 + (dr/dθ)2 dθ

r = f (θ) , α < θ < β

Note: since we will pick up a  dθ  from the ds we'll require to substitute one of the parametric equations in for x or y depending upon the axis of rotation.  This will frequently mean that the integrals will be rather unpleasant.


Related Discussions:- Surface area with polar coordinates

If pth term of ap is q and qth term is p. p.t its nth term, If the p th te...

If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans:    APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p

I need help, in 2000,nearly 18% of cars in north America were sliver. what ...

in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?

Polynomials in one variable, Polynomials In this section we will discu...

Polynomials In this section we will discuss about polynomials.  We will begin with polynomials in one variable. Polynomials in one variable Polynomials in one variable

Sketch the graph, Sketch the graph of                          y = ( x -...

Sketch the graph of                          y = ( x -1) 2  - 4 . Solution Now, it is a parabola .Though, we haven't gotten that far yet and thus we will have to select

Algebra ii, How do you graph a hyperbola?

How do you graph a hyperbola?

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd