6.1 Areas between Curves by SGLee - HSKim, YJLim
1-21. Find the area of the region, bounded by the given curves.
1. 
http://matrix.skku.ac.kr/cal-lab/cal-6-1-1.html
.
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.
http://matrix.skku.ac.kr/cal-lab/cal-6-1-1.html
.
4. 
. <= 적분구간 (0,1), integral 앞에 2*
5. 
.
6. 
.
7. 
. <= 적분구간을 (0,1) 수정
8. 
.
9. 
.
10. 
x=12 삭제
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11. 
.
13. 
.
14. 
.
15. 
.
16. 
.
17. 
.
18. 
.
19. 
.
20. 
.
21. y=cosx, y= (x-pi/2)*(x+pi/2) (which replace 
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. 
.
23. 
.
24-25. Approximate the area of the region bounded by the given curves using the Midpoint Rule with 
.
24. 
http://wiki.sagemath.org/interact/calculus#Numerical_integrals_with_various_rules
.
26-29. Determine the area of the region bounded by the curves.
26. 
.
27. 
.
28. 
.
29. 
.
30. Find the area of region defined by the inequalities 
.
.
31. Find the area enclosed by the loop of the curve with equation 
.
(Tschirnhausen's cubic.) http://en.wikipedia.org/wiki/Tschirnhausen_cubic
.
32. Find the area of the region bounded by the curve 
, the tangent line to this curve at 
, and the 
-axis.
http://matrix.skku.ac.kr/cal-lab/cal-6-1-32.html
.
33. Find the number 
such that the line 
divides the region bounded by
the curves 
and 
into two regions with equal area.
.
34. (a) Find the number 
such that the line 
bisects the area under the curve
.
(b) Find the number 
such that the line 
bisects the area in part (a).
.
.
35. Find the values of 
such that the area of the region enclosed by the parabolas 
and 
is 1944.
.
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. 
, 
.
.
. 
has solutions 
,
is positive where 
. 
.
, 
, 
