I need some guidance for this problem:

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Find the work needed to empty the horizontal cylindrical tank if it is full of water. The pump is 2 meters abovce the tank, the tank is 8 meters long (lying on its side), and ther radius of the cylinder is 2 meters.

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Here's what I have so far:

Since work = force * distance, I've gotten the distance as (7-y). The cross section is a rectangle witrh a lenth of 8 meters. To get the width of the rectangle, I used x^2+y^2=25. I solved for y and got: squareroot(25-y^2).

So, the area of the cross-section is 8*squareroot(25-y^2).

It's given by my book that water has a density of 9800 Newtons.

To get the equation of the force, I did: 9800*(7-y)*[8*squareroot(25-y^2)].

Am I supposed to integrate now with boundaries of -5 to 5?

I got stuck in the middle (after factoring out the constant) while trying to integrate it:

78400*[integral from -5 to 5](7-y)*[squareroot(25-y^2)].

I hope everything made sense....

Can someone check my work and help me? Thanks.

The answer is 43.1 million Joules, but I'm not sure how to get it.