✔ 最佳答案
Refer to the figure below.
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1.
₋₁∫² f(x) dx
= Area of ΔABC - Area of ΔCDE
= (1/2) × AB × BC - (1/2) × CD × DE
= (1/2) × 2 × 2 - (1/2) × 1 × 1
= 1.5
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2.
₂∫⁴ f(x) dx
= -[Area of rectangle DFGE - Semicircle with diameter EG]
= -[DF × DE - (1/2) π (EG/2)²]
= -[2 × 1 - (1/2)π(1)²]
= 0.5π - 2
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3.
₄∫⁷ f(x) dx
= -Area of ΔFHG + Area of trapezoid HIJK
= -(1/2) × FH × FG + (1/2) × (IJ + HK) × JK
= -(1/2) × 0.5 × 1 + (1/2)(1 + 2.5) × 3
= 5
₋₁∫⁷ f(x) dx
= ₋₁∫² f(x) dx + ₂∫⁴ f(x) dx + ₄∫⁷ f(x) dx
= 1.5 + (0.5π - 2) + 5
= 0.5π + 4.5