Math, asked by Anonymous, 4 months ago

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 itzmesweety
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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