Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 7.

Question

anonymous · Answer

@Michele_Laino

irishboy123 · Answer

@amistre64

amistre64 · Answer

what have we considered?

anonymous · Answer

@amistre64

amistre64 · Answer

there are a few ways to approach this, the most obvious to me is called shells

amistre64 · Answer

what is a formula for determining the lateral area of a cylindar?

anonymous · Answer

2πrh

amistre64 · Answer

good we can use this

our height varies between the functions

can you write me up a height function?

anonymous · Answer

the formula for shells or washers is dx=pi(R^2-r^2)h

amistre64 · Answer

im working shells,  2pi rh is fine

amistre64 · Answer

a shell is a cylindar .

anonymous · Answer

okay is the height function

h=2pi(r)
h=2pi(7)
h=14pi

amistre64 · Answer

no,  the height of an object is the distance from top to bottom

if t(x) and b(x) bound the height, then t(x) - b(x) define the height at a given x

what functions would we use for a top and bottom?

anonymous · Answer

i dont know where tx and bx are

amistre64 · Answer

they are on your  graph ....

draw a cylindar around x=7 to see it better

amistre64 · Answer

you should know the region that is getting spun around ..... what function make up the top and bottom of that region?

anonymous · Answer

attachment

anonymous · Answer

the function that is being spin around is y=x

amistre64 · Answer

you are no where near the region that needs to be spun ....

amistre64 · Answer

|dw:1430431130914:dw|

anonymous · Answer

|dw:1430427741359:dw|

anonymous · Answer

y = 0.5x^2

amistre64 · Answer

|dw:1430431233007:dw|