Question

The volume of the solid obtained by rotating the region enclosed by, x=0 y=1 and x=y^5, about the line y=1. Find the volume

Answer 1

all i need is the formula. from [a,b] V=()dx

Answer 2

man its been a while since i did this stuff. i got (5/6)*pi

Answer 3

the interval is from 0 to 1

Answer 4

so V=pi?dx

Answer 5

the radiuses are y^5

Answer 6

pi [y^5]^2

Answer 7

i got \[5\Pi/6\]

Answer 8

\[pi\int_{0}^{1}y^{10}\ dy\]
if i see it right

Answer 9

i have no idea why u have to the 10th

Answer 10

(y^5)^2 is the rotation

Answer 11

ohh you are using y^5, not fifth root of x. cool.

Answer 12

should it not be in terms of x since i have a dx?

Answer 13

no, the graph integral really doesnt care what you call it; the names are just to help us position it all

Answer 14

for some reason it is saying its wrong. I think it wants it in terms of x for my answer

Answer 15

\[\frac{\pi}{21}\]

Answer 16

i gotta see where my eyes went wrong at

Answer 17

i got (10/11)*pi ..

Answer 18

the radius function in terms of x will be: 1 - x^(1/5) right?

Answer 19

yes

Answer 20

\[\int\limits_{0}^{1}\pi(1-x^{1/5})^2dx\]
or
\[\int\limits_{0}^{1}2\pi y^5(1-y)dy\]

Answer 21

1 - x^(1/5)
1 - x^(1/5)
----------
1 - x^(1/5)
-x^(1/5) + x^(2/5)
--------------------
1 -2x^{1/5} + x^{2/5}

\[pi\int_{0}^{1} ( 1 -2x^{1/5} + x^{2/5})dx\]
\[pi (x -\frac{5x^{6/5}}{3} + \frac{5x^{7/5}}{7})\]
\[pi (1 -\frac{5}{3} + \frac{5}{7})\]

Answer 22

maybe?

Answer 23

we've all been out of the pre-calc game for too long!!

Answer 24

my first thought was mixing shells and discs lol