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Math Help - integrals area problem

  1. #1
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    Post integrals area problem

    Hello


    I need help to solve the problem in the picture below. I know the area A(13286039940) and the intercept(2.395E10) from the lower line(2.704).My problem is to find X,Y and area Dw1. Is it possible to do that with this given information? If yes how do I approach the problem?

    D = f(x)= (x/((11.08^0.3127340824*2899653^0.2153558052*e^20.700 37453)/0.8515))^(1/-0.9232209738)

    D invers = f(x)= ((e^20.70037453*x^-0.9232209738*11.08^0.3127340824* 2899653^0.2153558052)/0.8515)


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  2. #2
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    Opalg's Avatar
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    To avoid writing lengthy constants, I'll write the function f(x) as f(x) = kx^\alpha. Then Y = kX^\alpha, and the area A of the yellow rectangle is A = X(kX^\alpha-2704) = kX^{\alpha+1}-2704X. You know A and you want to solve this equation for X. You won't find an exact solution, but you should be able to use numerical approximation techniques to get a solution as accurate as you need.

    Having found X, you can get the blue area by integration. It is Dw1 = \int_X^{2395E+10}f(x)\,dx = \left[\frac{kx^{\alpha+1}}{\alpha+1}\right]_X^{2395E+10} = \frac k{\alpha+1}\bigl((2395E+10)^{\alpha+1} - X^{\alpha+1}\bigr).
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