A 200-foot tall dam (as pictured below) is to be built to hold back a river. If

Question

A 200-foot tall dam (as pictured below) is to be built to hold back a river. If the width of the dam at height x is given by the function g(x), which of the following integrals gives the total force on the dam? (Recall that the weight density of water is 62.5 pounds per cubic foot, and assume that the water goes all the way to the lop of the dam.) 62.5/200 integral^200_0 (200 - x)g(x) dx 62.5/200 integral^200_0 xg(x) dx 62.5 integral^200_0 (200 - x)(x)dx 62.5 intgeral^200_0 xg(x)dx 62.5/200 integral^200_0 g(x)dx 61.5 integral^200_0 g(x) dx It is impossible to tell from the given information.

Explanation / Answer

Depth= 200 - x
Width = g(x)

Area = (200 - x) * g(x)

Force = pressure * area

Force = 62.5 * (200-x) * g(x)

Now, we are to integrate over the height, i.e from x to 200

So, the answer is

Option C

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