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14 - Volume

# 14 - Volume - 9x 2 4y 2 = 36 Cross sections perpendicular...

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Volumes We used definite integrals to compute areas by making slices and adding up the areas of the slices. For volumes we will slice the solid into pieces whose volume can be approximated and then added together. Ex. Find the volume of a sphere of radius r.
Ex. A solid has slices perpendicular to the y axis that are squares with one edge in the xy plane. The intersection of the solid with the xy plane is the region between the curves x = y 3 – 9 and x = -2y 2 – 9. Find the volume of the solid.

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Ex. The base of S is an elliptical region with boundary curve
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Unformatted text preview: 9x 2 + 4y 2 = 36. Cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse in the base. Find the volume. Do. The base is a region in the xy plane bounded by y = x 2 and y = 4. Cross sections are perpendicular to the y-axis. Set up integrals to find the volume if the cross sections are: 1. half-circles 2. squares 3. isosceles right triangles. If you work the problems out, the answers are: 1. 4 ; 2. 32; 3. 8...
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