problem in webwork

The problem asks me to find the surface area of the line $y=2xe^{-8x}$ rotated around the line $x=-4$ with limits $x=2$ and $x=6$

the formula for surface area of a line rotated around a vertical line (as far as I know) is $$ \int_d^c 2π*f(y)*\sqrt{1+(dx/dy)^2} dy $$

However I cant make x the subject of the formula provided, and the program says that the limits of 2 and 6 are correct as shown in the image.

So is there another way to do this without having to make x the subject of the formula?

Frist time post so sorry for the formatting if it is bad

  • $\begingroup$ What is the meaning of $f(y)$? $\endgroup$
    – Andrei
    Commented Oct 7, 2021 at 18:36
  • $\begingroup$ f(y) is a function of Y e.g $x=\sqrt y $ $\endgroup$
    – AkAn
    Commented Oct 7, 2021 at 18:37
  • $\begingroup$ Think about what it represents - it should be a radius. But remember that you don't rotate around $x=0$, but instead you rotate around $x=-4$. $\endgroup$
    – Andrei
    Commented Oct 7, 2021 at 18:39


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