Find out the volume of the solid -x = (y - 2)2, Mathematics

Assignment Help:

Find out the volume of the solid obtained by rotating the region bounded by x =  (y - 2)2 and  y = x around the line y = -1.

Solution : We have to first get the intersection points there.

y =( y - 2)2

y = y 2 - 4 y + 4

0 =y 2 - 5 y + 4

0 = ( y - 4) ( y -1)

Therefore, the two curves will intersect at y = 1 & y = 4 . Following is a sketch of the bounded region and the solid.

2212_solid3.png

Following are our sketches of a typical cylinder. The sketch on the left is here to illustrates some context for the sketch on the right.

425_solid4.png

Following is the cross sectional area for this cylinder.

A ( y ) = 2 ∏ ( radius ) ( width )

=2 ∏ ( y + 1) ( y - ( y - 2)2 )

= 2 ∏ (- y3 + 4 y 2 + y - 4)

The first cylinder will cut in the solid at y = 1 and the final cylinder will cut in at y = 4 . Then the volume is

V=∫dc A(y)dy

=2 ∏∫4-y3 + 4y+ y- 4 dy

=2 ∏ (-(1/4) y4 + (4/3)y3+(1/2)y2 - 4y)|41

=(63 ∏/2)


Related Discussions:- Find out the volume of the solid -x = (y - 2)2

Determine that the following series is convergent or diverge, Determine or ...

Determine or find out if the following series is convergent or divergent. Solution In this example the function we'll use is, f (x) = 1 / (x ln x) This function is

Proof integral function, Proof of: if f(x) > g(x) for a x b th...

Proof of: if f(x) > g(x) for a x b then a ∫ b  f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop

Simplification, 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

What is universal set, A non-empty set or group of which all the sets under...

A non-empty set or group of which all the sets under concern are subsets is known as the universal set. In any part of application of set theory, all the sets under concern might l

Integerts, how do u add and subtract integers

how do u add and subtract integers

Rationalize the denominator, Rationalize the denominator for following.  Su...

Rationalize the denominator for following.  Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica

Direct and inverse variation, A man can do a piece of work in 25 days how m...

A man can do a piece of work in 25 days how many people are required to complete same work in 15 days?

Understanding Logistics, How can i get a better understanding of logistics ...

How can i get a better understanding of logistics without having a degree on logistics and knowledge of it? Simply, in a very basic form..

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