integration?
2016-04-10 5:45 am
find the values of c such that the area of the region bounded by the parabolas y=x^2-c^2 and y=c^2-x^2 is 576
回答 (1)
2016-04-10 7:36 am
y=x^2-c^2 i
y=c^2-x^2 ii
i=ii
x^2-c^2=c^2-x^2
2x^2=2c^2
x=c or x=-c
area=2 int(-c to c)|(x^2-c^2)-(c^2-x^2)|dx
area=4 int(0 to c)|2x^2|dx
area=(8/3)x^3 |0 to c
576=(8/3)c^3
c=6
y=c^2-x^2 ii
i=ii
x^2-c^2=c^2-x^2
2x^2=2c^2
x=c or x=-c
area=2 int(-c to c)|(x^2-c^2)-(c^2-x^2)|dx
area=4 int(0 to c)|2x^2|dx
area=(8/3)x^3 |0 to c
576=(8/3)c^3
c=6
收錄日期: 2021-04-18 14:43:38
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https://hk.answers.yahoo.com/question/index?qid=20160409214501AAi6R4u