For what values of m do the line y = mx and the curve y =
x
x
2 + 1
enclose a region? Find the
area of the region.
Answers
Answered by
12
Answer:
The two curves meet at
mx=x−x
2
orx
2
=x(1−m)∴x=0,1−m
∫
0
1−m
(y
1
−y
2
)dx=∫
0
1−m
(x−x
2
−mx)dx=[(1−m)
2
x
2
−
3
x
3
]
0
1−m
2
9
if m < 1or (1−m)
3
[
2
1
−
3
1
]=
2
9
or (1−m)
3
=27
∴m=−2
But if m > 1 then 1 - m is negative then
[(1−m)
2
x
2
−
3
x
3
]
1−m
0
=
2
9
−(1−m)
3
(
2
1
−
3
1
)=
2
9
∴−(1−m)
3
=−27 or 1−m=−3∴m=4
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