1. Find the area, S, enclosed by the curve y=x^3-3x^2+2x and the x-axis.
2. Find the area. S. enclosed by the curve y= -x^2+2x+3 and the line y=x+1.
Maths Area Questions
2010-01-15 11:32 pm
回答 (1)
2010-01-16 3:21 am
✔ 最佳答案
第1題:y=x^3-3x^2+2x與y=0交點, x=0, 1, 2
so, A=∫[0~2] |x^3-3x^2+2x| dx
=∫[0~1] (x^3-3x^2+2x) dx - ∫[1~2] (x^3-3x^2+2x)dx
= (1/4)-1+1 - [ (15/4)-7+3 ]= 1/2
第2題:
y=-x^2+2x+3與y=x+1交點, x= -1, 2
so, A=∫[-1~2] [(-x^2+2x+3)-(x+1)]dx
=∫[-1~2] (-x^2+x+2)dx
= -3+3/2+6= 9/2
收錄日期: 2021-05-02 00:05:39
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