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

Cubic math, A fish tank has the base area of 45 cm3 and is filled to the de...

A fish tank has the base area of 45 cm3 and is filled to the depth of 12 cm.If the height is 25 cm then how much more will be needed to fill the rest of the tank?

Example of spiral development of the mathematics curriculum?, E1) Can you g...

E1) Can you give some more examples of the spiral development of the mathematics curriculum? E2) A Class 3 child was asked to add 1/4 + 1/5. She wrote 2/9. Why do you feel this

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

Evaluating functions, Next we have to talk about evaluating functions.  Eva...

Next we have to talk about evaluating functions.  Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at

Mean and standard deviation, Q. Mean and Standard Deviation? Ans. ...

Q. Mean and Standard Deviation? Ans. The normal distribution is totally described if we know the average and standard deviation. - the population mean of the distribu

External division of section formula, give me the derivation of external di...

give me the derivation of external division of sectional formula using vectors

Find relation between x and y while lies on straight line, Find the relatio...

Find the relation between x and y when the point (x,y) lies on the straight line joining the points (2,-3) and (1,4) [ Hint: Use area of triangle is 0] Ans :   Hint: If the poi

Prove that 7cot - 3cosec = 3, If 7 cosec?-3cot? = 7, prove that 7cot? - 3co...

If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans:    7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C

Solve sin (3t ) = 2 trig function, Solve sin (3t ) = 2 . Solution T...

Solve sin (3t ) = 2 . Solution This example is designed to remind you of certain properties about sine and cosine.  Recall that -1 ≤ sin (θ ) ≤ 1 and -1 ≤ cos(θ ) ≤ 1 .  Th

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