Find out the surface area of the solid - parametric curve, Mathematics

Assignment Help:

Find out the surface area of the solid acquired by rotating the following parametric curve about the x-axis.

x = cos3 θ

y = sin3 θ

 0 ≤ θ ≤ ?/2

Solution

We will first require the derivatives of the parametric equations.

dx/dt =  -3 cos2 θ sin θ

 dy/dt = 3sin2 θ cos θ

 Previous to plugging into the surface area formula let us get the ds out of the way.

ds = √ (9 cos4 θsin2 θ + 9 sin4 θ cos2 θ) dt

= 3|cosθ sin θ| √ (cos2 θ + sin2 θ)

=3 cos θ sin θ

Note that we could drop the absolute value bars as both sine and cosine are positive in this range of θ given.

 Now let us get the surface area and do not forget to as well plug in for the y.

774_Find out the surface area of the solid - Parametric Curve.png


Related Discussions:- Find out the surface area of the solid - parametric curve

Prove that bd/cd = bf/ce, In the given figure, ∠AEF=∠AFE and E is the mid-p...

In the given figure, ∠AEF=∠AFE and E is the mid-point of CA. Prove that BD/CD = BF/CE Ans:    Draw CG ¦DF In ΔBDF CG ¦ DF ∴ BD/CD = BF/GF     .............(1)

Limits, Limits The concept of a limit is fundamental in calculus....

Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some

Differentiate inverse tangent functions, Differentiate the following functi...

Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b)  y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other

Managment Science, Classify models based on the degree of their abstraction...

Classify models based on the degree of their abstraction, and provide some examples of such models.

Example of factoring quadratic polynomials, Factor following polynomials. ...

Factor following polynomials.                               x 2 + 2x -15 Solution x 2 +2x -15 Okay since the first term is x 2 we know that the factoring has to ta

How many cousins does robert have- miscellaneous math, Bonnie has twice as ...

Bonnie has twice as many cousins as Robert. George has 5 cousins, which is 11 less than Bonnie has. How many cousins does Robert have? Work backwards to find the solution. Geor

Analysis and optimization, 1. In an in finite horizon capital/consumption m...

1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production

Indices, What is a way to solve indices

What is a way to solve indices

HELP, A local pizza shop sells large pies for $7 each. If the cost of the o...

A local pizza shop sells large pies for $7 each. If the cost of the order is proportional to the number of pizzas would they charge a delivery charge per pizza or per order ?

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