IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

surajp

hey can u giv me som tips on solving area under curves problems faaster??

avinash.sharma

Please see the reference question http://www.goiit.com/posts/list/6235.htm

Q : please explain me about the area under a parabola x ² =4y^and the circle equation x²+y²=16

Solution :

The method is very simple and can be used with any two curves.

1. Get points of intersection of curves - in this case parabola and circle.

2. Now see in the figure that movement of y is from 0 to (-2+2 5) is along the curve x^2 = 4y and from (-2+2 5) to 4 is along the circle so the desired area is the sum of these two.

= _{[ 0]} ^{[ -2+2 5]} (2 y) dy + _{[-2 + 2 5 ]} ^{[ 4]} 16-y^2) dy . Double this area as the figures are symmetric.

rishikesh_anshu you have included some extra are indicated in figure 2.

Arjun are including area of parabola twice by addtion the equations.

It's a good practice that you should use the axis where we have to calculate less figures in this question if we use x axis then we have to calculte area of three regions as indicated in figure 2 by different shades.

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