课程名称︰微积分甲上
课程性质︰必修
课程教师︰周青松
开课学院：理学院
开课系所︰地质科学系 生物环境系统工程系 生物产业机电工程系 工管系科管组
考试日期（年月日）︰103/12/1
考试时限（分钟）：50分钟
试题 :
(1) (20 pts)
Find the integral of f(x) = 2sin^3x + 3sinx from [-π, π]
and sketch the graph on [-π, π]
(2) (20 pts)
Let f be continuous on [a,b] ,
define F(x) = ∫x f(t) dt and G(x) = ∫x f(t) dt, for c,d in [a,b]
c d
Show that F and G differ by a constant.
Show that F(x) – G(x) = ∫d f(t) dt
c
(3) (20 pts)
(a) Find g(x) = ∫x f(t) dt, (b) Sketch the graphs of f, g
-2
(c) Where is f continuous, differentiable? Where is g differentiable?
(4) (20 pts)
Find f from the information given: f''(x) = cosx, f'(0) =1, f(0)=2
(5) (20 pts)
Calculation d/dx ∫(x^2+2) 1/(2+√t ) dt and d/dx∫2x t√(1+t^2) dt
√x tanx