Calculus-Sec-6-1-Solution

6.1   Areas between Curves                         by SGLee - HSKim, YJLim

1-21. Find the area of the region, bounded by the given curves.

1.

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4.

.             <= 적분구간 (0,1), integral 앞에 2*

5.

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6.

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7.

.                  <= 적분구간을 (0,1) 수정

8.

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9.

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10.      x=12  삭제

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11.

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12.

has solutions ,

so  is positive where

13.

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14.

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16.

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18.

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19.

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20.

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21.  y=cosx, y= (x-pi/2)*(x+pi/2) (which replace

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integral(cos(x) - (x-pi/2)*(x+pi/2), x, 0, pi/2) Answer: 1/12*pi^3 + 1 ).

22-23. Find the integral and interpret it as the area of a region.

22.

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23.

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24-25. Approximate the area of the region bounded by the given curves using the Midpoint Rule with .

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26-29. Determine the area of the region bounded by the curves.

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27.

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28.

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29.

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30. Find the area of region defined by the inequalities .

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31. Find the area enclosed by the loop of the curve with equation .

(Tschirnhausen's cubic.) http://en.wikipedia.org/wiki/Tschirnhausen_cubic

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32. Find the area of the region bounded by the curve , the tangent line to this curve at , and the -axis.

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33. Find the number  such that the line  divides the region bounded by

the curves  and  into two regions with equal area.

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34. (a) Find the number  such that the line  bisects the area under the curve

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(b) Find the number  such that the line  bisects the area in part (a).

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35. Find the values of  such that the area of the region enclosed by the parabolas  and  is 1944.

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For  and    is another solution.

Therefore .

36-40. Find the area of the region bounded by the given curves.

36.

Since ,

37.

Since

38.

Since

39.

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