mid 4th.pdf - Math292 Spring 2018 PRINT your name PRINT...

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Math 292 , Spring 201 8 PRINT your name: PRINT your name: : Question Points Score 1 13 2 16 3 8 4 8 5 15 6 8 7 16 8 16 Total: 100 Show all of your reasoning and work for full credit, unless indicated otherwise. Use full mathematical or English sentences. You have 90 minutes and the exam is 100 points. You do not need to simplify numerical expressions. For example leave fractions like 100 / 7 or expressions like ln(3) / 2 as is. For multiple choice questions, circle the correct answer. Notation: following the book, we use boldface to denote vectors, e.g., a , b are vectors.
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Math 2 92 Calc 3 Spring 201 8 1. (13 points) Short answer questions. (a) (5 pts.) Let R = [0 , 2] × [0 , 2]. Use a Riemann sum with m = n = 2 to estimate the value of RR R x + y dA . Take the sample points to be the lower left corners. (b) (3 pts.) Let the density function of a lamina D be ρ ( x, y ) = x 2 y . Use a double integral to write a formula for the mass of the lamina D . (c) (5 pts.) Let F = h x, y, z i , and C be a curve parameterized by r ( t ) = h t, e t , sin t i , 0 t 1. Set up, but DO NOT evaluate the line integral
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