Question

The graph of the equation 2x=y^2 from A(0,0) to B(2,2) is revolved about the x-axis.The surface area of the resulting solid (in square units and to three decimal places) is:

Answer 1

18.088
21.322
3.3934
18.585
22.062

Answer 2

@iambatman

Answer 3

@freckles

Answer 4

is that really what is written?
like what equation are they talking?

Answer 5

I am sorry I fixed the error. It is = not +

Answer 6

ok do you know the surface area formula ?

Answer 7

no

Answer 8

I'm going to assume your stuff is bounded by 2x=y^2 and y=0 and the points you gave


anyway you should know the formulas at least
you might want to use these notes in the future http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx


but anyways I decided to put this integral in terms of y since it seemed easier since were rotating about the x-axis and your equation x=1/2*y^2 is already solved for x

just find your limits now (these are actually already given )
\[\int\limits_{c}^{d}2 \pi y \sqrt{1+(\frac{dx}{dy})^2} dy \]

Answer 9

The limits are 0 and 2 right?

Answer 10

yep

Answer 11

So does the equation become: integral (2,0) (2piy(sqrt(1+2x/y^2)^2)dy

Answer 12

@freckles

Answer 13

how did you get dx/dy to be a function of x and y?

Answer 14

dx/dy should just be a function of y

Answer 15

\[x=\frac{1}{2} y^2 \\ \frac{dx}{dy}= ? \text{ use power rule } \]

Answer 16

1/y?

Answer 17

2-1=1 not -1

Answer 18

\[\frac{dx}{dy}=\frac{1}{2} \cdot 2 y^{2-1}=\frac{2}{2}y^{1}=1y^1=y^1 =y\]

Answer 19

So if dx/dy =y. Then the equation becomes integral (0,2) (2piy(sqrt((1+(sqrt2x))^2))dy

Answer 20

how are you getting that

Answer 21

replace dx/dy with y

Answer 22

\[\int\limits\limits_{c}^{d}2 \pi y \sqrt{1+(\frac{dx}{dy})^2} dy \\ \int\limits_0^2 2 \pi y \sqrt{1+(y)^2} dy \]

Answer 23

you can drop the ( ) around the y
since y is just one term

Answer 24

When I integrated that I got 4 π y sqrt(1+y^2)

Answer 25

looks like you just multiplied the integral by 2

Answer 26

that isn't integration

Answer 27

you might want to try a substitution before the actual integration

Answer 28

let u=1+y^2
du/dy=2y

Answer 29

I made an error. I did dx instead of dy. I got 21.322 when I tried again.

Answer 30

sounds much better

Answer 31

Thank you very much!