Find the area of the surface obtained by rotating the curve y= 1+2 x^2
from x=0 to x = 9 about the y-axis

Question

Find the area of the surface obtained by rotating the curve y= 1+2 x^2
from x=0 to x = 9 about the y-axis

amistre64 · Answer

thats for volume

amistre64 · Answer

area of the surface might mean surface area

anonymous · Answer

yea - i assumed thats what caro required - oh i see what you mean!

anonymous · Answer

i cant remember the SA formula

@ caro9999  which is it ?

amistre64 · Answer

|| 2pi y ds

amistre64 · Answer

opps for y rotation, 

|| 2pi x ds

amistre64 · Answer

solve limits and inverse so that everything speaks in terms of x=

amistre64 · Answer

y= 1+2 x^2

sqrt((y-1)/2) = x

when x=0, y=1
         x=9, y=163

amistre64 · Answer

$$\int_{9}^{163}2pi\ \sqrt{\frac{y-1}{2}}\sqrt{1+(\frac{1}{4\sqrt(\frac{y-1}{2})})^2}\ dy$$

amistre64 · Answer

these things are horrible!!  where you getting these from?

anonymous · Answer

Calc 2, I know they are the death of me right now lol

amistre64 · Answer

$$\int_{9}^{163}\pi\ \sqrt{2y-2}\sqrt{1+\frac{1}{8y-8}}\ dy$$

$$\int_{9}^{163}\pi\ \sqrt{\frac{8y-7}{4}}\ dy$$

$$\frac{\pi}{16 }\int_{9}^{163}8\sqrt{8y-7}\ dy$$

almost got something, may not be right but i can dbl chk it with thte wolf

turingtest · Answer

am I doing this wrong$$S=2\pi\int_{0}^{9}x\sqrt{1+16x^2}$$?this should not be too hard
..or am I having one of those days where I am talking nonsense?

amistre64 · Answer

8(8y-7)^(1/2)  --> 2(8y-7)^(3/2)/3

2pi(8(136)-7)^(3/2)/48 - 2pi(8(9)-7)^(3/2)/48 = 4583.803...

now for the dbl chk :)

amistre64 · Answer

this is rotated about the y, not the x

turingtest · Answer

isnt that$$2\pi\int xds$$?

amistre64 · Answer

yes, ds is sqrt(1+x'^2)

amistre64 · Answer

since we are given y=; we have to convert to to x=

turingtest · Answer

yeah..wait, why do we have to covert it?

amistre64 · Answer

so that we have the x and the ds in terms of x

turingtest · Answer

I'm confused...
 wolf your answer and I'll do mine and we'll see what happens I guess

amistre64 · Answer

or rather, to make the y the independant

anonymous · Answer

4583.803 didn't work :/

amistre64 · Answer

4583.96 is the wolfs on mine

turingtest · Answer

mine was supposed to be 6114.2
I hope you have multiple tries

amistre64 · Answer

or a button that gives it the finger lol

amistre64 · Answer

i wonder if this is simpler in polars

experimentx · Answer

2 * pi * y * dx
y = 1+2 x^2

turingtest · Answer

it's
2*pi*x*ds
that much we agree on

anonymous · Answer

Yup, @TuringTest 6114.2 worked!

turingtest · Answer

oh yeah ...
groovy

anonymous · Answer

Thanks for your help guys!!

turingtest · Answer

welcome, I hope you understood the process!

experimentx · Answer

oo .. along the x axis!!