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

Finding the inverse of a function , Finding the Inverse of a Function : Th...

Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh

Heat loss in a cylindrical pipe, which laws of physics are used to discuss ...

which laws of physics are used to discuss heat loss in a pipe

Regression, Regression line drawn as y=c+1075x, when x was 2, and y was 239...

Regression line drawn as y=c+1075x, when x was 2, and y was 239, given that y intercept was 11. Caculate the residual

String art, finding distance using circumference

finding distance using circumference

Power of iota, The next topic that we desire to discuss here is powers of i...

The next topic that we desire to discuss here is powers of i. Let's just take a look at what occurring while we start looking at many powers of i . i 1 = i

Probability distributions, Probability Distributions Since the value of...

Probability Distributions Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the varia

Rounding, what is the result if 816.537 is rounded to the nearest tenth

what is the result if 816.537 is rounded to the nearest tenth

Error in measurement, what is actual error and how do you find percentage e...

what is actual error and how do you find percentage error

Algorithm for division helping a child grasp, E1) Why don't you think of so...

E1) Why don't you think of some activities for the same purpose now? E2) Suggest, in detail, another activity for helping a child grasp the algorithm for division. We come to

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