Calculating Work Done by a Steam Engine Using Integral Calculus

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this is a question about a steam engine with the equation (sorry for lack of proper math language)

PV^1.4 = k (constant)


using the idea of integral from V1 to V2

ie...


the amount of work done is W=(int.V1 to V2) PdV

Where P1=160lbs/in^2
and V1 = 100 in^3...V2=800 in^3

solving for P we can find P=kV^(-1.4)...where k is 100953.1751

now i solved for in the integral

160*(100953.1751) *[ .4 V^.4] from 100 to 800 (for V)

i found W=9.35 * 10^11


Did i do this properly?
thanks for the help.
 
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it's okay...i figured out where i went wrong
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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