http://i729.photobucket.com/albums/ww291/kaka1307/0070.jpg
thanks a lot!
更新1:
pls show clear steps~
f.5 definite integration
2010-11-20 6:38 am
Find the total area of the shaded region(ans: 67/8)
http://i729.photobucket.com/albums/ww291/kaka1307/0070.jpg
thanks a lot!
http://i729.photobucket.com/albums/ww291/kaka1307/0070.jpg
thanks a lot!
回答 (2)
2010-11-20 6:56 am
2010-11-20 6:51 am
1 The intersection points are (1,0) and (7/2,-5/4)
For the first region, the area is
∫ (x^2-5x+4)-(-x^2+4x-3) dx [x from 0 to 1]
=∫ (2x^2-9x+7) dx
=(2/3)x^3-(9/2)x^2+7x | [0,1]
=19/6
the area of the second shaded region is
∫ (-x^2+4x-3)-(x^2-5x+4) dx [x from 1 to 7/2]
=∫ (-2x^2+9x-7) dx
=(-2/3)x^3+(9/2)x^2-7x | [1,7/2]
=(49/24)-(-19/6)
=125/24
The total area is
19/6+125/24
=67/8
For the first region, the area is
∫ (x^2-5x+4)-(-x^2+4x-3) dx [x from 0 to 1]
=∫ (2x^2-9x+7) dx
=(2/3)x^3-(9/2)x^2+7x | [0,1]
=19/6
the area of the second shaded region is
∫ (-x^2+4x-3)-(x^2-5x+4) dx [x from 1 to 7/2]
=∫ (-2x^2+9x-7) dx
=(-2/3)x^3+(9/2)x^2-7x | [1,7/2]
=(49/24)-(-19/6)
=125/24
The total area is
19/6+125/24
=67/8
收錄日期: 2021-04-23 20:48:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101119000051KK01447