I am working on a problem involving a semicircular tank underground, and how much work is required to pump water out of the top. i set everything as i see correctly, but cannot computer the definite integral. i only know basic substitution and to some degree integration by parts, but that is apparently not required for this problem. the integral i am having problems with is (def integral, from zero to 2, of) [(3-y)(sqrt(4y - y^2))] dy.(adsbygoogle = window.adsbygoogle || []).push({});

i narrowed it down to the fact i can't integrate sqrt (4y - y^2), which i found out is incredibly difficult and complicated. so i'm thinking there is either an easier way to inegrate this that i'm unaware of, or a way to set the problem up so that i'm not dealing with square roots. i have been working on this for over 5 hours now, in the past two days, with no good results.

the problem is something like this. semicircular tank underground, lenght of 8, radius of 2. the tank is laying horizontal to the horizon, with the flat part of the semicircle at the top. there is a nozzle 1 ft high that the water has to go through.

i set it up like this:

work = force x distance = volume x density x acceleration due to gravity x distance.

so i computed the dimensions of the slab, 8 * dy * 2(sqrt[4y - y^2])

multiplied this by 62.5 (density of water), 32 (accel. of gravity), and (3-y) (distance the slab of water travels, (2-y)+1, since there is a 1 ft nozzle).

this left me with 32000 times the inegral i listed above. sorry this is so long, but i'm really stuck with this one. thanks for any advice

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# Work problem, easier inegral?

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