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Unformatted text preview: OASIS PRACTICE MIDTERM EXAM MATH20B Turn off and put away your cell phone. No calculators or any other devices allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly & legibly; no credit will be givenfor illegible solutions. If any question is not clear, ask for clarification. But don't be a dumbass. Talking to you, Mike. 1. Evaluate the following integrals (3 points) J cos(4X)sin'14X) dx 2. Evaluate the integral (3 points) 3. Find the setup for the area of the region bounded by the curves y=sin(2x) and y=sin(x), as shown on the graph. You do not need to evaluate the integral. (3 points) 4. The velocity is given as V(t)= t - 3 and it acts within the time of 1and 4 seconds. a. (3 points) Find the displacement b) (3 points) Find the distance travelled. 5. Find the number c, such that the area under y = x3 between x (3 points) = 1and x = c equals 9· 6. Find the setup for the volume of the triangle revolving about x graph. Do not evaluate. (5 points) = -1, as show on the -, 7. Find the area of one loop, defined as r = 2sin(39). Evaluate completely. (6 points) 8. Evaluate the integral (3 points) d dx i X3 tan ([-2) dt ~12 9· Givenr3 J 0 f(x) dx =7 and 14 J 4 f(x) dx = 2 Do not evaluate. a. If f(x) dx is odd, findJ -3 f(x) dx b. Iff(x) dxis even, findf J..l f(x) dx 10. Find the volume of the region between the curves y = X2 and y2 = x if the region is sliced perpendicular to the x-axis by squares. Do not evaluate. (5 points). 11. In 3 sentences or less, please explain why you are such a douche, whereas Howie is so cool. Is it an inversely proportional equation? (1 million points) ...
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