嘉定一中AP选修课
AP Calculus BC
课程概览
Microeconomics
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Midterm Test 2
Midterm Test 2
期中测试2 (Units 5-7)
期中测试，覆盖积分、积分应用、积分技巧等Units 5-7的内容
✍️ 7 题
1. ∫ x²eˣ dx = ?
A. eˣ(x² - 2x + 2) + C
B. x²eˣ + C
C. eˣ(x² + 2x) + C
D. (x²/2)eˣ + C
2. The area between y = x² and y = x is:
A. 1/6
B. 1/3
C. 1/2
D. 1/12
3. The volume of the solid obtained by rotating y = √x around the x-axis from x=0 to x=4 is:
A. 8π
B. 16π
C. 4π
D. 2π
4. ∫ sin²(x) dx = ?
A. x/2 - sin(2x)/4 + C
B. x/2 + sin(2x)/4 + C
C. sin(x)cos(x) + C
D. x - sin(2x)/2 + C
5. ∫ dx/(x²+4) = ?
A. (1/2)tan⁻¹(x/2) + C
B. tan⁻¹(x/2) + C
C. (1/2)arctan(x) + C
D. ln(x²+4) + C
6. Using the Shell Method, the volume of y = x² rotated about the y-axis from x=0 to x=2 is:
A. 8π/3
B. 4π
C. 16π/5
D. 2π
7. ∫₀³ x²√(9-x²) dx is evaluated by the substitution x = 3sin(θ). The integral becomes:
A. 81∫ sin²(θ)cos²(θ) dθ
B. 9∫ sin²(θ) dθ
C. 81∫ cos²(θ) dθ
D. 27∫ sin(θ)cos(θ) dθ
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