Volume of solid of revolution using washer method with horizontal axis

[Lo.Lee.Ta.]

1. Find volume between f(x) = x, g(x)= sin(sqrt(5x+3)), x=1, and x=2, when revolved around y=4.


2. Would it be correct to write the integral like this?

∫1 to 2 of [$\pi$(4 - sin(√(5x + 3))² - $\pi$(4 - x)²]


I am using the washer method, and for the gap that's in the middle I usually think about it by saying r= inner curve - axis of rotation.
R= outer curve - axis of rotation

But in this case the axis of rotation is above the function, so would it be r= 4 - inner curve

and R= 4 - outer curve?

Thanks! :)

 

[Lo.Lee.Ta.]

Please answer!

 

[haruspex]

∫1 to 2 of [$\pi$(4 - sin(√(5x + 3))² - $\pi$(4 - x)²]

Yes, that's right. You ought to check that the curves do not cross within the range.

 

[JPaquim]

Yes, the inner radius should be 4 - inner curve and the outer radius should be 4 - outer curve. I think your setup is correct.

 

[Lo.Lee.Ta.]

:D Thanks so much, haruspex and JPaquim! :D