課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：理學院
開課系所︰地質科學系 生物環境系統工程系 生物產業機電工程系 工管系科管組
考試日期（年月日）︰103/12/1
考試時限（分鐘）：50分鐘
試題 :
(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