Please find the value of the definite integral thanks.
x=100000(9√y-1)
x=100000((9√y-1)/(8√y))
First, find out for what values of y, that these two equations equal.
$\displaystyle 9\sqrt{y}-1=\frac{(9\sqrt{y}-1)}{8\sqrt{y}}$
$\displaystyle 1=8\sqrt{y}$
$\displaystyle y=\frac{1}{64}$
Also, note that when $\displaystyle y=\frac{1}{81}$, the equations are both equal to zero. We now have our limits, so let's continue to integration...
Graphs are positive, so take the difference between the equations to get: $\displaystyle 100000(9\sqrt{y}-1)(\frac{1}{8\sqrt{y}}-1) = 100000(\frac{9}{8}-9\sqrt{y}-\frac{1}{8\sqrt{y}}+1)$
Now, integrate it...
$\displaystyle \int _{\frac{1}{81}}^{\frac{1}{64}} 100000(\frac{9}{8}-9\sqrt{y}-\frac{1}{8\sqrt{y}}+1) dy $
Can you finish this?