嘉定一中AP选修课
AP Calculus BC
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Microeconomics
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Assignment 7: Techniques of Integration
Assignment 7: Techniques of Integration
积分技巧
练习积分技巧：分部积分、三角替换、部分分式
✍️ 5 题
1. ∫ x·eˣ dx = ?
A. xeˣ - eˣ + C
B. eˣ(x - 1) + C
C. xeˣ + eˣ + C
D. eˣ + C
2. ∫ ln(x) dx = ?
A. x·ln(x) - x + C
B. x·ln(x) + x + C
C. ln(x)/x + C
D. 1/x + C
3. Which substitution is best for ∫ dx/√(x²+9)?
A. x = 3·tan(θ)
B. x = 3·sin(θ)
C. u = x² + 9
D. x = √9·sec(θ)
4. ∫ dx/(x²+1) = ?
A. tan⁻¹(x) + C
B. arctan(x) + C
C. ln(x²+1) + C
D. Both A and B
5. To integrate 1/((x+1)(x-2)), use:
A. Partial fractions: A/(x+1) + B/(x-2)
B. u-substitution
C. Integration by parts
D. Trig substitution
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