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Practice Test 4b

# Practice Test 4b - with vertices(1 1(2 1 and(1 2 about the...

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Practice Test IV B for Math 1501, Calculus I Problem 1: A solid is generated by rotating a square of sidelength a about its diagonal. Compute its volume. Problem 2: Find the volume of one of the smaller wedges that is cut from a spherical shell of inner radius 1 / 2 and outer radius 1 by two planes that meet at a diameter with an angle π/ 6. Problem 3: Compute the volume of the solid that is generated by rotating the triangle
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Unformatted text preview: with vertices (1 , 1) , (2 , 1) and (1 , 2) about the x –axis. Problem 4: A tank in the form of a half sphere of radius 5m is sitting on a pole of height 10m. How much work is needed to ﬁll the tank with water? (Use g = 10m / s 2 .) Problem 5: Compute the following integrals. Z 2 x √ x + 1 d x Z ln x x 2 d x Z 2 1 ln x x d x Z π sin 2 x cos 2 x Z ln 2 e x 1 + e x d x...
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