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

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

What is the probability in which she gets heads further flip, Jennifer ?ipp...

Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o

SYSTEMS OF ODE, Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear s...

Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi

Interpretation of r – problems in interpreting r values, Interpretation of ...

Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th

Applied mathematics, I have a journal article in applied mathematics and wa...

I have a journal article in applied mathematics and want to analyze the solutions step by step. Is there anyone specialize in this file?

An initial species population , An initial species population is y(0) = 300...

An initial species population is y(0) = 3000. At t=0 the population starts to grow exponentially with a doubling time of 2 years. Mark the only correct statement: a)    The per

What is the continuously compounded forward rate, At time t an investor s...

At time t an investor shorts a $1 face value zero coupon bond that matures at time T = t and uses the entire proceeds to purchase a zero coupon bond that matures at time

Sketch the parametric curve for parametric equations, Sketch (draw) the par...

Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par

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