Question

what is common between 5x-2 plzzzzzzz tell me plzzzzzzz​

Answer 1

Area common to the curves 5x

2

=0 and 2x

2

+9=0 is equal to

A 12✓3

Given curves

y=5x

2

⇒x

2

=

5

y

....(1)

which is a parabola opening upward having vertex at (0,0)

Other curve is 2x

2

+9=y .....(2)

⇒x

2

=

2

y−9

which is a parabola having vertex at (0,9).

Now, solving eqn (1) and (2), we get

5x

2

=2x

2

+9

⇒3x

2

=9

⇒x=±

3

⇒y=15

Point of intersection of the curves is (−

3

,15) and (

3

,15)

Required area =2(arOAB)

$$=2 \int ^\sqrt 3 _0 (y_1-y_2)dx$$

$$= 2 \int ^\sqrt 3 _0 \{ (2x^2 + 9) - 5 x^2\} dx$$

$$ 2 \int ^\sqrt 3 _ 0 (9-3x^2) dx$$

$$ = 2 \left( 9x - 3 \displaystyle \frac{x^3}{3}\right) ^\sqrt3 _0$$

=2(9

3

−3

3

)=12

3

sq. units

solutionRelated Questions to study

The area between the parabolas y

2

=4a(x+a) and y

2

=−4a(x−a) in sq. units isConsider two curves C

1

:y=

x

1

andC

2

:y=ℓnx on the xy plane. Let D

1

denotes the region surrounded by C

1

,C

2

and the lines x=1 and D

2

denotes the region the region surrounded by C

1

,D

2

and the line x=a. If a D

1

=D

2

then the value of

′

a

′

-