Question

Need help finding region bounded by the curve y=sqrt(x). medal and fan (:

Answer 1

notes

Answer 2

yeah ill be rotating around the y axis for the first question so I have to use this formula

Answer 3

am i integrating from 0 to 4?

Answer 4

Yup, to find the area.

Answer 5

Sorry, I got that picture wrong....

Answer 6

https://www.desmos.com/calculator/toasem5dyi

Answer 7

Right, so its the upper region, and because you are integrating by dy you would be integrating from 0 to 4, and you the equation would be: x = y^2

Answer 8

so im doing \[\int\limits_{0}^{4}\pi(y^2)^2dy\]

Answer 9

Yes that works.

Answer 10

but i get 4piy^4

Answer 11

You have: \[\int\limits_{0}^{4}\pi*y ^{4}dy= \pi*\int\limits_{0}^{4}y ^{4}dy\]

Answer 12

Then you take the integral of that and put in the limits and you get your answer.

Answer 13

ok got it. thanks! my last question would be rotating around the x-axis

Answer 14

so im using the washer formula correct?

Answer 15

Yes you would be, because the answer would have a hole in the middle.

Answer 16

\[\int\limits_{a}^{b}\pi((upper limit)^{2}-(lower limit)^{2})^{2}dy\] Right? and the upper and lower limits are with respect to the x axis.

Answer 17

ok so upper limit is y^2

Answer 18

lower limit..?

Answer 19

Look at the area that you are solving for.
My first drawing was wrong sorry about that.