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更新1:
y=? ......
y=∫ √(- x2 + 6x + 16) + 2 dx
2011-07-12 12:33 am
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回答 (2)
2011-07-12 9:23 am
✔ 最佳答案
∫(－2 to 8)_√(－x^2+6x+16)+2dxSol
－x^2+6x+16
=－(x^2－6x+9)+25
=－(x－3)^2+5^2
x=3+5Sinw
－x^2+6x+16
=25－(3+5Sinw－3)^2
=25Cos^2 w
dx=5Coswdw
∫(－2 to 8)_√(－x^2+6x+16)dx
=∫(－π/2 toπ/2)_｜5Cosw｜5Coswdw
=25∫(－π/2 toπ/2)_Cos^2 wdw
=(25/2)∫(－π/2 toπ/2)_1+Cos(2w)dw
=25π/2+(25/4)Sin(2w)|(－π/2 toπ/2)
=25π/2
∫(－2 to 8)_√(－x^2+6x+16)+2dx
=25π/2+20
2011-07-12 1:01 am
20+25pi/2??
收錄日期: 2021-04-30 15:54:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110711000016KK06551