Unformatted text preview: WORKSHEET 34 - Fall 1995 1. Sketch the finite area whose boundary is composed of pieces of the curves x = 1 − y 4 and x = y 2 − 1. a) Find the area of this region by integrating with respect to y . b) Find the area of this region by integrating with respect to x . 2. Sketch the region of the xy-plane bounded by the positive x-axis, the positive y-axis, and the curve y = 4 − x 2 . Consider the solids obtained by revolving this region around: a) the x-axis; b) the y-axis; c) the line x = − 1; d) the line x = 2; e) the line y = − 1; f) the line y = 4. For each of these six solids set up two integrals for the volume, one in x , that is integrating “ dx ,” and one in y , that is, integrating “ dy .” For each integral state whether it represents the “shell,” “disc,” or “washer” method. Example for ??: Z 2 π (4 − x 2 ) 2 dx, disc method Z 4 2 πy p 4 − y dy, shell method 3. Suppose you have a tent which is supported by two flexible aluminum poles which run along the ceiling3....
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- Spring '08
- Highest point, rectangular tent ﬂoor, ﬂexible aluminum poles, disc method shell