HOW TO FIND AREA OF THE CIRCLE WHICH IS INTERIOR TO THE PARABOLA
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
4x2+ 4y2 = 9 ------------------- (1)
and x2 = 4y -------------------(2)
Reducing (1) to standard form by dividing 4 .we get
x2+ y2 = (3/2)2
Ist of all draw figures of both the circle and the parabola in cartesian plane.
4x2+ 4y2 = 9 ------------------- (1)
and x2 = 4y -------------------(2)
Reducing (1) to standard form by dividing 4 .we get
x2+ y2 = (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 ' x2 ' from (2) in (1) we get
4(4y)+ 4y2 = 9
16y + 4y2 - 9 = 0
4y2 - 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= 土⇃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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