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Math 1B Due date: Monday 21 March Name: _________________________ Take Home Quiz 2 Please show all your work on a separate sheet of paper. Neatly do the problems in order and leave enough space between problems for my comments and grading. You are allowed to get help with the problems and discuss them with your classmates but all work must be your own. 1. Evaluate each integral. a) b) c) 1 2 ∫ x cos(π x)dx ∫ tan θ sec θ dθ ∫ cos (3x)dx 0 3 π 4 4 0 d) ∫ e) ∫ x2 dx 9 − x2 5x 2 − 3x + 2 dx x 3 − 2x 2 2. Consider dx ∫ x(1+ x 2 ) a) Evaluate the integral using a trig substitution. b) Evaluate the integral using partial fractions. 3. The region bounded by the curve y = ln x , the line x = e , and the x-axis is revolved about the xaxis. Find the volume of the solid that is generated. 4. A tank is half full of water. Set up the integral to find the work done in emptying out the water by € € the top of the tank. a pump located 3 m above The tank is shaped like a triangular candy box. The top and bottom of the tank are triangles with height 20 m and base 10 m. The tank itself is 10 m high.