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Unformatted text preview: the area of the region. x = 2-y 2 , x = y 6.1 #19 Sketch the region bounded between the given curves and then ﬁnd the area of the region. y = sin x , y = sin 2 x , x = 0, x = π 6.1 #24 Sketch the region bounded between the given curves and then ﬁnd the area of the region. y = e x , y = 1 2 e x + 1 2 , x =-2, x = 2 6.1 #31 Imagine a cylindrical fuel tank of length L lying on its side; the ends are circular with radius b . Determine the amount of fuel in the tank for a given level by completing these steps: a. Explain why the volume of the tank may be modeled by V = 2 L Z b-b p b 2-y 2 dy 2 b. Explain why the volume of fuel at level h (-b ≤ h ≤ b ) may be modeled by V ( h ) = 2 L Z h-b p b 2-y 2 dy c. Finally, for b = 4 and L = 20, numerically compute V ( h ) for h =-3 ,-2 , . . . , 4. Note: V (0) and V (4) will serve as a check on your work. 3...
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- Spring '08
- Math, Tank, Region