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Simpson's rule for a volume problem

uploaded imageThe portion ofthe graph y = tan−1 x between x = 0 and x = 1 is rotated around the y axis to form a container. The container is filled with water. Use n = 6 subintervals andSimpson's rule to approximate the work required to pump all of the water out over the side of the container. Give your answer in decimal form.

(Distance is measured in meters, the density of water is 1000 kg/m3, and use 9.8 m/s2 for g.)

I am setting this up using x = tan y, W = F*d, F = m * a, a = 9.8, m = V * density

V = integral of (pi)(tan y)^2 dy

So it looks like this: W = 9800(pi) * integral from 0 to (pi/4) of (tan(y))^2 dy

Not getting the right answer. (using online calculator for simpson's rule, so that should be right). Anyone see where I am possibly setting it up wrong?

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Answer #1
the integral should be 0 to pi/4 of tan^2(y)*(pi/4-y)?
answered by: clifford
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