Find out the area under the parametric curve, Mathematics

Assignment Help:

Find out the area under the parametric curve given by the following parametric equations.

 x = 6 (θ - sin θ)

y = 6 (1 - cos θ)

0 ≤ θ ≤ 2Π

Solution

Firstly, notice that we've switched the parameter to θ for this problem.  This is to ensure that we don't get too locked into all time having t like the parameter.

Here now, we could graph this to confirm that the curve is traced out exactly just once for the given range if we wanted to. We are going to be making out at this curve in more detail after this instance so we won't draw its graph here.

Actually there isn't very much to this instance other than plugging the parametric equations into the formula. We'll first require the derivative of the parametric equation for x though.

dx / dΠ = 6 (1 - cosΠ)

after that the area is,

A = ∫0 36 (1-cos θ)2

= 36 ∫0 1- 2 cos2 θ dθ

= 36 ∫0 3/2 - 2 cosθ + ½ cos (2θ) dθ

= 36 (3/2 θ-2sin θ  + ¼ sin (2θ)) |2Π0

= 108 Π

 


Related Discussions:- Find out the area under the parametric curve

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?

Show that the height h of the tower, The angle of elevation of the to...

The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α. On advancing 'p' meters towards the foot of the tower, the angle of eleva

Properties of vector arithmetic, Properties of Vector Arithmetic If v, ...

Properties of Vector Arithmetic If v, w and u are vectors (each with the same number of components) and a and b are two numbers then we have then following properties. v →

Division problem, Raul has 56 bouncy balls. He puts three times as many bal...

Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does

Regression - measures of relationships, Regression - Measures of Relationsh...

Regression - Measures of Relationships - It is a concept that refers to the changes which happen in the dependent variable as a result of changes happens on the independent va

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