Find c>0 so that the area bounded by y=x^2 - c and y = c - x^2 equals to 9?

my ans : 9 = INT of (c-x^2) - (x^2-c) dx


9= INT 2c - 2X^2 dx





I am confused. should we need the limit of the integral??


what can we solve without knowing the limit..

Find c%26gt;0 so that the area bounded by y=x^2 - c and y = c - x^2 equals to 9?
by solving the two equations we get their point of intersetion...... we get the limits from -sqrt c to + sqrt c





so int(c-x^2)dx - int ( x^2-c) = 9





we get (8c sqrt c)/3 = 9





solving we get c^3 = 729 / 64





that means c = 9/4
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Reply:2.25
Reply:You can solve it without the limit by chopping it into 4 pieces and integrating with respect to y.


9 = A = 4int(0 to c)y^1/2 dy


= (8/3)y^3/2(0 to c)


= (8/3)c^3/2


c = (27/8)^(2/3)


= 9/4
Reply:Consider what the limits WOULD be. With respect to x, the limits would be where the two curves intersect, right? So try setting the curves equal to each other...





x^2-c=c-x^2


x^2=c


x=plus or minus sqrt(c)





so the limits would be sqrt(c) and -sqrt(c).





Does that help?