HOW TO FIND AREA OF THE CIRCLE WHICH IS INTERIOR TO THE PARABOLA

##
**Area Under Curves**

Let us write two equations of circle and parabola respectively

4x

and x

Reducing (1) to standard form by dividing 4 .we get

x

Ist of all draw figures of both the circle and the parabola in cartesian plane.

4x

^{2}+ 4y^{2 }= 9 ------------------- (1)and x

^{2 }= 4y -------------------(2)Reducing (1) to standard form by dividing 4 .we get

x

^{2}+ y^{2 }= (3/2)^{2 }Ist of all draw figures of both the circle and the parabola in cartesian plane.

As it can be seen from figure both curves intersect each other at two points say A and A' .

Next we have to find these two coordinates points of intersection . Solving (1) and (2) to find the values of x and y

Putting the value of ' x

^{2 }' from (2) in (1) we get

4(4y)+ 4y

^{2 }= 9

16y + 4y

^{2 }- 9 = 0

4y

^{2 }- 16y -9 = 0

y = (-16+20)/8 and (-16-20)/8

y = 1/2 and -9/2

So Rejecting the -ve value of y ,because when we put negative value (-9/2) in eq (2) , we shall have two complex values of "x" which are not acceptable.

so only put positive value (1/2) of 'y' in (2) we get two real values of 'x' such that x= åœŸ⇃2,

Now we can write coordinate M(⇃2,0) and N (-⇃2,0)

Required Area = Shaded area

=

**2 × Area OBAO**

**Note this step carefully**↑

Multiplying every terms with 2 which is written at beginning of the previous line.

Putting the values of
upper and lower limits of x

ALSO READ

**HOW TO INTEGRATE INTEGRAL WITH SQUARE ROOT IN NUMERATOR**

## Final words

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Nice post. I learned some new information. Thanks for sharing.

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