MATH 115 Midterm: MATH 115 UPenn 115Fall 04Post Exams
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5 feet, with the center at ground level. It is full of water from the bottom to ground level. Remember that the weight of water is 62. 4 pounds per cubic foot: (11 points) solve this inde nite integral, (11 points) solve this integral, (11 points) solve this integral: Part b: (13 points) find a power series representation for. Find a number a > 0 such that for x [ a, 0], |ex t3(x)| 10 4: (12 points) find the length of the curve y = , for 1 x 2: (12 points) find the area of the surface generated by rotating the curve ln x. 4 about the x-axis, where x lies between 1 and 3. y = x3: (12 points) suppose that a parametric curve is de ned by the following equation. x(t) = tet y(t) = sin(t) Write an integral which represents the length of the curve between t = 1 and t = 2.
