Processing math: 100%
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 ⟶
y2−4=0 ⟶
(y+2)(y−2)=0 ⟶ y=−2 or y=2
Now see the given graph of the enclosed region.
Using horizontal cross-sections to describe this region, we get that
−2≤y≤2 and y2≤x≤4 ,
so that the area of this region is
AREA=∫2−2(Right − Left) dy
=∫2−2(4−y2) dy
=(4y−y33)|2−2
=(4(2)−(2)33)−(4(−2)−(−2)33)
=(8−83)−(−8+83)
=16−163
=483−163
=323
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