Mathematics
partial fraction decomposition

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Final Answer

Hello!

We have to compute the integral of pi*y^2(x) dx at the given range.
Note then at this range x>0 and 7-x>0.

y^(x) = 49/(7x - x^2) = 49/[x(7-x)] = 7*(1/x + 1/(7-x)).

So V = pi*int_0.75_6_[7*(1/x + 1/(7-x)]dx = 7pi*[lnx - ln(7-x)]_0.75_6 =

7pi*ln[x/(7-x)]_0.75_6 = 7pi*(ln(6) - ln(3/25)) =

7pi*ln(50).

Please ask if anyting is unclear.

Borys_S (8128)
UT Austin

Anonymous
Really helpful material, saved me a great deal of time.

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