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MATH 152 Activity 5 (6.4-8.2) Directions: Put your group name, section number and members present on one answer sheet. Use scratch paper for work, meaning only put the answers on the answer sheet. Turn in only ONE answer sheet per group. No calculators allowed, however you may use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is expected. 1. Write (but do NOT compute) an integral to find the area enclosed by y = 1 − x2 and y = x2 + x. . 2. Given f (x) = 3x2 −2x, find all values c ∈ [−1, 1] such that f (c) = favg , the average value of f on this interval. . 3. Answer: ˆ sin2 x cos2 x dx. Calculate . 4. Answer: Answer: ˆ 2 x ln x dx. Compute 1 . 5. Answer: A 15-Newton weight is suspended vertically at the end of a 30 m long rope. The rope weighs 6 Newtons. How much work (in N-m) is required to pull the weight to the top? . 6. Given function f and g with 0 ≤ g(x) ≤ f (x) on the interval 0 ≤ x ≤ 2, write an integral to compute the volume of the solid formed by rotating the region bounded by y = f (x), y = g(x), x = 0, and x = 2 about the line y = −1. . 7. Answer: ˆ Calculate 2 . Answer: 4 x2 x dx. +3 Answer: 1