Question

Determine the volume of the solid obtained by rotating the portion of the region bounded by and that lies in the first quadrant about the y-axis.

Answer 1

your trying to tempt me arent ya :)

Answer 2

Nope. Not in the least. ;)

Answer 3

is this saying the volume of the first quadrant spun around the y axis?

Answer 4

Yup. Which is to say, bound by both axis with the limits being each intersection

Answer 5

i appear to be missing a function to determine proper bound lol; or have gone blind :)

Answer 6

Oh you're right they didn't post... My bad! It's y=(x^1/3) and y =x/4

Answer 7

x^3 = x/4 would be the bounds then right...

Answer 8

cbrt(x)=x/4 typoed it lol

Answer 9

im going with 0 to 4

Answer 10

gotta redo that lol

Answer 11

0 to 8 ...

Answer 12

Yeah try again lol

Answer 13

There you go

Answer 14

my stupidity got in the way

Answer 15

I forgive you. 64 is awfully close to one. ;)

Answer 16

spin around the y axis....

Answer 17

we can do this from 0 to 2 on the y right

Answer 18

Less bored?

Answer 19

lol nerds!

Answer 20

less.... :)

Answer 21

Yes, if you mean in terms of y.

Answer 22

one radius is x=4y the other is .....

Answer 23

y^3?

Answer 24

I wouldn't do it that way.

Answer 25

\[\pi \int\limits_{0}^{2} [4y]^2 - [y^3]^2 dy\]

Answer 26

Though yes. You can. The top one being?

Answer 27

why is it gonna break?

Answer 28

Haha no,but yeah that's right. Let's pretend y just put inthe calculator and got it right because you can push buttons well. :)

Answer 29

i get 128/3 - 128/7

Answer 30

512/21 = 24.381 ??

Answer 31

if I do shelss; i wonder if i get the same result :)

Answer 32

That was fun :) it's 512 pi/21you forgot pi lol

Answer 33

i think i dropped a pi lol

Answer 34

ack!!.... yeah, just realized it :)

Answer 35

76.59 closer?

Answer 36

yes!! shell and disk are the same yay!!

Answer 37

\[2\pi \int\limits_{0}^{8} x(x^{4/3}) -x(\frac{x}{4}) dx\] = 76.59