# Area bounded by the two curves

#### ProBasket

Find the area bounded by the two curves:
$$x=100000(5*sqrt(y)-1)$$
$$x=100000(\frac{(5*sqrt(y)-1)}{(4*sqrt(y))})$$

i'm having alot of trouble trying to find the lower and upper limit of the two functions. I tried setting the two functions together and solving for y, but i get 0. then trying to plug in 0 for y which gives me -100000 for the first function, but you cant plug in 0 for y for the second function.

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#### Davorak

Well first you should know that you have to solve for y:
$$5 \sqrt{y}-1=\frac{5\sqrt{y}-1}{4\sqrt{y}}$$
so
$$20y-4\sqrt{y}=5\sqrt{y}-1$$
$$20y+1=9\sqrt{y}$$
square both sides and:
$$400y^2+40 y+1=81 y$$
$$400y^2-41 y+1= 0$$
Then use the quadractic equation to find the overlaping area. After that intgrate(one function minus the other) between the two values of y.

Also you could put these equations in terms of y(x) rather then x(y) and follow the same procedure and obtain the same answer.

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