Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$$y = 1 + sec\;x,\;y =3,\;about\;y=1$$

How is the inner-radius of the cross-section $sec\;x$? Why isn't it $1 + sec\;x?$

  • $\begingroup$ Because you're revolving about the line $y=1$. $\endgroup$ – paw88789 Sep 12 '14 at 1:45
  • $\begingroup$ Will you please elaborate? $\endgroup$ – Jamie Kudla Sep 12 '14 at 1:45
  • $\begingroup$ Did you do the sketching step? That may help. Also I am assuming you are only looking at one branch of the secant function, although that is not clear from the problem's statement. $\endgroup$ – paw88789 Sep 12 '14 at 1:49
  • $\begingroup$ Yes,I have the correct graph in front of me. Every problem I've done up to now the inner-radius has just been the curve. You said it was because it's revolving around y=1, does that mean if it revolved around y=2 the inner-radius would be [(1 + secx) -2]? $\endgroup$ – Jamie Kudla Sep 12 '14 at 1:57

Draw a rectangle representing the direction the function will rotate around the given line/axis.

Its easy to see that the rectangle formed will have the width $\delta x$ and height $y+1 - 1 = (\sec x + 1)- 1 = \sec x$

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