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136Probs6.1 - the area of the region x = 2-y 2 x = y 6.1#19...

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These are the problem statements for the suggested problems for 5.8. In general, you will get the problems from the textbook, but I will post questions until everyone has a textbook. 6.1: 1,3,5,9,12,13,15,19,24,31 6.1 #1 Sketch a representative vertical or horizontal strip and find the area of the given regions bounded by the curves y = - x 2 + 6 x - 5 y = 3 2 x - 3 2 6.1 #3 Sketch a representative vertical or horizontal strip and find the area of the given regions bounded by the curves y = sin 2 x on [0 , π ] y = 0 6.1 #5 Sketch a representative vertical or horizontal strip and find the area of the given regions bounded by the curves x = y 2 - 5 y x = 0 1
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6.1 #9 Sketch the region bounded between the given curves and then find the area of the region. y = x 2 , y = x 3 6.1 #12 Sketch the region bounded between the given curves and then find the area of the region. y = 4 x 2 - 9, x = 3, x = 0, y = 0 6.1 #13 Sketch the region bounded between the given curves and then find the area of the region. y = x 4 - 3 x 2 , y = 6 x 2 6.1 #15 Sketch the region bounded between the given curves and then find
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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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