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21b_ps8

# 21b_ps8 - Co-21B Problem Solving#8T 1 Find the centroid of...

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Co-21B Problem Solving #8T 1) Find the centroid of the region bounded by y = 1 x , y = 0 , x = 1 and x = 2 . *Answer: 1 ln 2 , 1 4 ln 2 ( ) 2) Consider the region R bounded by y = 1 ! x 2 and the x -axis. a) Find the centroid of the region R. *Hint: Use symmetry to find one of the coordinates! *Answer: 0, 2 5 ( ) b) Use Pappus’s Theorem to find the volume of the solid formed when R is revolved about the line x = 4. Check your answer using shells 3) Show that the surface area of y = x 3 , (1 ! x ! 2) revolved about the x -axis is the same as y = x 3 , (1 ! x ! 8) revolved about the y -axis. b)Then find the area. 4) Find the area of the surface generated by revolving y = 2 x + 1 , 1 ! x ! 7 about the x -axis. 5) Use Pappus’s Theorems to find the volume and surface area of the torus formed by revolving x 2 + ( y ! 5) 2 = 4 about the x -axis. 6) Remember that Pappus’s Theorem can give you an alternative method to find the centroid of a region: a) Find the volume of the solid formed by revolving the region bounded by y = x 2 and y = 1 about the x -axis.
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