definite intergration
2011-05-20 2:43 am
圖片參考：http://img850.imageshack.us/img850/7373/99251634.jpg
The figure shows two shaded regions boundedby the curve y=(x^2)-6, y=x and the x-axis. Find the area of the shadedregions.
回答 (2)
2011-05-20 4:33 am
2011-05-20 4:18 am
First, find the intersection points of the 2 curves
y=x---------(1)
y=x²-6-----------(2)
Sub (1) in (2)
x²-6=x
x²-x-6=0
(x-3)(x+2)=0
x=-2 or 3
y=-2 or 3
∴The intersecting points are (-2,-2) and (3,3) respectively
Then it is easy to observe that the x-intercepts are √6 and -√6 respectively
Area of shaded region=√6(3+2)/2=5√6/2 [Since the shaded region is triangle]
y=x---------(1)
y=x²-6-----------(2)
Sub (1) in (2)
x²-6=x
x²-x-6=0
(x-3)(x+2)=0
x=-2 or 3
y=-2 or 3
∴The intersecting points are (-2,-2) and (3,3) respectively
Then it is easy to observe that the x-intercepts are √6 and -√6 respectively
Area of shaded region=√6(3+2)/2=5√6/2 [Since the shaded region is triangle]
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110519000051KK00636