課程名稱︰微積分甲上
課程性質︰大一必修
課程教師︰朱樺
開課學院：工學院
開課系所︰材料系、電機系
考試日期（年月日）︰2014/12/15
考試時限（分鐘）：50 min
試題 :
CALCULUS MID-QUIZ 2
Instructor: Professer Huah Chu
Quiz date: December 15,2014
Quiz time: 50 minutes
Total score: 42 points(Each problem is worth 7 points)
1. Find
d^2 x^2 dt
----- (∫----------------)^2
dx^2 0 (1-2t^3)^(1/2)
2. Evaluate
ln(1+x^2)
∫------------- dx
x^2
3. Evaluate
sinθ
∫------------- dθ
3 + 4tanθ
4. Evaluate
∫(1+(1+(x)^(1/2))^(1/2))^(1/2) dx
5. Evaluate
xdx
∫-----------------
(4x^2+8x+13)^2
6. Let p and q be rational numbers. Prove that ∫x^p(1-x)^q dx is an
elementary fuction.
(a) If p is an integer
(b) If q is an integer
(c) If p+q is an integer
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