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

Title expressions equivalent, 2x40 420x4 7x240 84x20 Explain h...

2x40 420x4 7x240 84x20 Explain how three expressions are equivalent.

Trig, what is the domain of the function f(x)= 2x^2/x^2-9

what is the domain of the function f(x)= 2x^2/x^2-9

What does required to earn on his further science test in 93, Justin earned...

Justin earned scores of 85, 92, and 95 on his science tests. What does he required to earn on his further science test to have an average (arithmetic mean) of 93%? To earn an a

., WRITE the condition that should be fulfilled by two matrices A&B to get ...

WRITE the condition that should be fulfilled by two matrices A&B to get the product AB and BA

Payoff Matrix, A farmer grows apples on her 400-acre farm and must cope wit...

A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"

Assignment help job, Sir before I applied for online assignment help job an...

Sir before I applied for online assignment help job and the selection process is not complete for me. You sent me problem assignment before.But those problems were not completed.Ca

Operation research, discuss the sequencing decision problem for n jobs on t...

discuss the sequencing decision problem for n jobs on two and three machines

Physics of medical imaging, A radiograph is made of an object with a width ...

A radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm. The object being imaged is 15 cm from the

Correlation and regression, 1. Using given data set (Assignment_1data in th...

1. Using given data set (Assignment_1data in the folder) a) Make scatterplot between "Years since first marriage" and "Total children ever born" b) Make scatterplot between

Partial Differential Equation, Consider the wave equation u_tt - u_xx = 0 w...

Consider the wave equation u_tt - u_xx = 0 with u(x, 0) = f(x) = 1 if -1 Please provide me a detailed answer. I had worked the most part of this question and the only I would like

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