Page 209 - How To Solve Word Problems In Calculus
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Think of each vertical rectangle as having (mnemonically) length
8 − y and width dx. Its area is (8 − y) dx. The total area of the
region is
2
A = (8 − y) dx
0
2
3
= (8 − x ) dx
0
4 2
x
= 8x −
4 0
= (16 − 4) − 0
= 12
(b)
y = 8
8 8
(x,y)
3
x = √ y
1 1 2 2
Using horizontal rectangles, the length of each rectangle is x and
the width is dy. We integrate with respect to y from0to8.
8
√
3
A = xdy y = x is equivalent to x = 3 y
0
8
√
3
= ydy
0
8
= y 1/3 dy
0
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