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Math 1210-001 Homework 9 Due 22 July, 2013 This homework assignment is designed to go along with sections 4.2 through 4.5 of your textbook, which we have completed in class. Make sure your work is neat, legible, well-organized and self-explanatory. You must staple your assignment to receive full credit. Name: R5 1. (10 points) Use the definition of the definite integral to calculate 0 (x + 1) dx. R1 R2 R1 R2 2. (10 points) Given that 0 f (x) dx = 3, 1 f (x) dx = −2, 0 g(x) dx = 10, and 1 g(x) dx = 3, R0 calculate 2 [g(x) − f (x)] dx by first writing the desired integral in terms of the given integrals, and then substituting the given values. Z 3 x2 + 1 √ 3. (10 points) Calculate dx. x3 + 3x 1 Z π (sin x + cos x) dx. (A direct computation will 4. (10 points) Use symmetry to evaluate −π receive no more than 5 points.) 5. (10 points) Find the average value of f (x) = tan x sec2 x on the interval [0, π4 ].