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2
/4
22
s
i
n
2
sin
0.091.
24
Ly
y
ydy
L
π
ππ
⎛⎞
⎛
⎞
=−
=
⎜⎟
⎜
⎟
⎝⎠
⎝
⎠
∫
(c) For the region
3 /4
Lx
L
≤≤
, we obtain
3/
4
4
2
s
i
n
2
sin
0.82
y
L
⎛
⎞
=
⎜
⎟
⎝
⎠
∫
which we could also have gotten by subtracting the results of part (a) and (b) from 1; that
is, 1 – 2(0.091) = 0.82.
14. We follow Sample Problem 393 in the presentation of this solution. The integration
result quoted below is discussed in a little more detail in that Sample Problem. We note
that the arguments of the sine functions used below are in radians.
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 Spring '08
 Any
 Physics

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