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

Find out a vector that is orthogonal to the plane, A plane is illustrated b...

A plane is illustrated by any three points that are in the plane.  If a plane consists of the points P = (1, 0,0) , Q = (1,1,1) and R = (2, -1, 3) find out a vector that is orthogo

Discret math, i have a question about discret math

i have a question about discret math

Trig identities, What is the exact vale of sin(theta/2) when sintheta=3/5, ...

What is the exact vale of sin(theta/2) when sintheta=3/5, pi/2

Direction field for the differential equation, We require to check the deri...

We require to check the derivative thus let's use v = 60. Plugging it in (2) provides the slope of the tangent line as -1.96, or negative. Thus, for all values of v > 50 we will ha

Functions, the function g is defined as g:x 7-4x find the number k such tha...

the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2

Rate and ratio, express 4:24 as fraction in lowest term

express 4:24 as fraction in lowest term

How to creates factor by substitution, How to creates Factor by Substitutio...

How to creates Factor by Substitution ? Can you factor this polynomial? x 2 + 3x + 2 (For this tutorial, I'm going to assume that you know how to do some basic factorin

Determine the line parallel or perpendicular, Determine if the line that pa...

Determine if the line that passes through the points ( -2, -10) and (6, -1) is parallel, perpendicular or neither to the line specified  by 7 y - 9 x = 15 . Solution Togive

If the area of the parallelogram is 36 m2 what is the height, The height of...

The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m 2 , what is the height in meters? Let x = the measure of the base a

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