Math, asked by manedipesh143p, 8 months ago

Find area bounded by parabola
y = 4x – x2 and x-axis.​

Answers

Answered by dkyadav94
1

Step-by-step explanation:

First, we need to find where the two functions intersect.

4

x

x

2

=

x

x

2

4

x

+

x

=

0

x

2

3

x

=

0

x

(

x

3

)

=

0

x

=

0

and

x

=

3

So our interval of integration is

0

x

3

y

=

4

x

x

2

is a parabola that is concave down

y

=

x

is the line that passes through the origin with slope 1

The integral for the area is

4

x

x

2

x

d

x

=

3

x

x

2

d

x

integrating we have

3

2

x

2

1

3

x

3

Evaluating at we have

(

3

2

)

3

2

(

1

3

)

3

3

0

=

27

2

27

3

=

27

2

9

81

6

54

6

=

27

6

=

9

2

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