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SOLUTION 17: Compute the area of the region enclosed by the graphs of the equations x=y2 and x=4 . Begin by finding the points of intersection of the two graphs. From x=y2 and x=4 we get that y2=4   y24=0   (y+2)(y2)=0    y=2  or  y=2 Now see the given graph of the enclosed region.

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Using horizontal cross-sections to describe this region, we get that 2y2  and  y2x4 , so that the area of this region is AREA=22(Right  Left) dy =22(4y2) dy =(4yy33)|22 =(4(2)(2)33)(4(2)(2)33) =(883)(8+83) =16163 =483163 =323

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