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Unformatted text preview:at distance x from the thin end the thickness is 10 mm + 1 1 , 000 x . Assume further that the rope has a density of 2000 kg/m 3 . The rope is hanging down vertically and you want to reel it in. Calculate how much work needs to be done when (a) the thinner end is on top, (b) the thicker end is on top. (Use the letter g in your answer instead of a numerical value). 6. Find an antiderivative of the function f ( x ) = x tan( x 2 ). 7. Evaluate the indefinite integral Z t √ 4-t 2 dt .