Co-21B Problem Solving #8T 1) Find the centroid of the region bounded by y=1x, y=0, x=1and x=2. *Answer: 1ln 2,14 ln 2()2) Consider the region R bounded by y=1!x2and the x-axis. a) Find the centroid of the region R. *Hint: Use symmetry to find one of the coordinates! *Answer: 0,25()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=x3, (1!x!2)revolved about the x-axis is the same as y=x3, (1!x!8)revolved about the y-axis. b)Then find the area. 4) Find the area of the surface generated by revolving y=2x+1, 1!x!7about the x-axis. 5) Use Pappus’s Theorems to find the volume and surface area of the torus formed by revolving x2+(y!5)2=4about 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=x2and y=1about the x-axis.
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