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

Constructing a dfa/nfa or a regex), Let ∑ = (0, 1). Define the following la...

Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege

Trigonometry, Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

How many people should she expect not to show, Laura is planning her weddin...

Laura is planning her wedding. She expects 230 people to attend the wedding, but she has been told that around 5% typically don't show. About how many people should she expect not

Parallelogram, fig angles of a irregular polygons exterior and interior .

fig angles of a irregular polygons exterior and interior .

Which of the following could not be the translation, If the expression 9y -...

If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c

Geometry, all basic knowledge related to geometry

all basic knowledge related to geometry

What is the measure of its width if its length is 3 inches, The perimeter o...

The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width? Let x = the width of the rectangle. Let x + 3 = th

Geometry, geometry fbw = 128 saf= 104 what is rfd

geometry fbw = 128 saf= 104 what is rfd

Operation research, advantages of vogel''s approximation method over north ...

advantages of vogel''s approximation method over north west corner method

Geometric mean-geometric progression, Geometric mean - It is a measure ...

Geometric mean - It is a measure of central tendency normally utilized to measure industrial increases rates. - It is explained as the nth root of the product of 'n' observa

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