课程名称︰微积分甲上 课程性质︰暑修 课程教师︰周青松 开课学院：理学院 开课系所︰数学系 考试日期（年月日）︰2010/7/22 考试时限（分钟）：50分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : It's necessary to explain all the reasons in detail and show all of your work on the answer sheet. Or you will NOT get any credits. If you used any theorems in textbook or proved in class, state it carefully and explicitly. 1. Assume that f is continunous and 注:试卷continunous疑为continuous误写 x ∫ f(t)dt = sinx - x cosx 0 (a) Determine f(π/2). (b) Find f'(x). 2. Let { x + 2, -2≦x≦0, f(x) = { 2, 0＜x≦1, { 4 - 2x, 1＜x≦2. x And set g(x) = ∫ f(t)dt. -2 (a) Carry out the integration. (b) Where is f continuous? Where is f differentiable? Where is g differentiable? d 4 3. (a) Calculate ──( ∫ sint^2dt ). dx tanx d x^2 + x dt (b) Calculate ──( ∫ ────── ). dx x^(1/2) 2 + t^(1/2) 4. Evaluate the integral π/4 ∫ ( x^2 - 2x + sinx +cos2x )dx. -π/4 --

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