Question

The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?

Answer 1

https://gyazo.com/9ccb696779c5a1339d9c084cfe54d9e5

@freckles

Answer 2

@Zarkon

Answer 3

@IrishBoy123

Answer 4

\[\int\limits_{0}^{\pi} \pi[\sin(\sin (x))]^2 dx \]

Answer 5

\[A(x)=\pi r^2\]

Answer 6

I am getting 5.435 x 10^-5
Which is obviously wrong

Answer 7

@zepdrix Are you aware of what must be done for this question?

Answer 8

Sec, lemme see if I can work it out :)

Answer 9

Ok thanks

Answer 10

Hmm your integral looks correct :o
Where did you get the numerical value from?
I don't think this integral has a nice closed-form solution.

So I guess you have to use some type of algebra calculator or something?
Wolfram seems to give us the correct answer:
https://www.wolframalpha.com/input/?i=integral+of+pi+sin%5E2%28sinx%29+from+x%3D0+to+x%3Dpi

Answer 11

I used my calculator to save me some time.

Answer 12

Ya you would have to do that for this problem :)
Maybe some trouble inputting it with your brackets and all that?
Cause your setup looks good.

Answer 13

I entered it as above

Answer 14

Maybe the way you entered it into wolfram is more appropriate, let me try.

Answer 15

Wolfram is pretty good at interpreting words

Answer 16

Does the mode matter?

Answer 17

The boundaries of your integral are radian measure.
Hmm, so yes, maybe.

Answer 18

I'm getting a data type error. Is there a way to insert sin^2?

Answer 19

sin^2(sin(x)) is the same as (sin(sin(x)))^2
so maybe try that second way
oh, I guess that's what you had in the first place though.

Answer 20

Yeah, I had that. Tells me wrong value or variable type.

Answer 21

Notice that Wolfram's exact solution involves the Bessel function of the first kind.
So maybe your calculator can't handle fancy stuff like this one.
I'm not sure :\

Answer 22

LOL
I can't use wolfram when taking my exam doe, they proctor my online course exam at school, when my own teacher tells me I can cheat.

Answer 23

hmm true >.<

Answer 24

I'm just gonna use it and tell em my calculator is acting up so I'm using an online one.

Answer 25

Thanks man

Answer 26

ya np
sorry we couldn't figure out the calculator :\
maybe ask teacher for assistance

Answer 27

Quick question if you don't mind.

Answer 28

and don't worry about it

Answer 29

I have a questions extremely similar to this one but has an equilateral triangle instead. Would I follow same steps but use the area formula of the triangle?

Answer 30

Oh wait, that one is cross sections.....it's different

Answer 31

maybe post the question? :)
If I can look at it, it might refresh my memory

Answer 32

Ok, I'll tag you soon.