Let Q be the region in the first quadrant bounded by f x ...

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Calculus
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Chapter 5 / Exercise 4
Calculus
Stewart
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w2014 8.2 Supplement: Finding Volumes by Cylindrical Shells Name(s) ______________________________________________________________ section # ______ We’ve already learned the disk/washer method for finding volumes of solids of revolution. Here, we will learn a second method called “cylindrical shells” or simply “the shell method.” In this method, instead of stacking thin disks or washers, we nest thin cylindrical shells one inside the other to create our volume. 1. Let Q be the region in the first quadrant bounded by f ( x ) = x 4 , the y axis, and the line y = 16. Here, we’ll use the shell method to write an integral which represents the volume of the solid generated when Q is revolved about the line y = 19. Step 1 . Sketch region Q. Step 2 . Inside region Q, draw a thin strip parallel to the axis of revolution (y=19). Call the length of this strip, “h,” and its vertical thickness, “ y.” This “h” is essentially the height of our cylindrical shell. Step 3 . Draw a line joining the top of the strip to the axis of revolution at y = 19. Call the length of this segment, “r.”
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Calculus
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Chapter 5 / Exercise 4
Calculus
Stewart
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