Does anyone know how to solve for part 3 on this question? ?

2020-06-22 11:27 am
I've got the first 2 answers correct, but the last part I keep messing up on.

回答 (2)

2020-06-22 2:17 pm
✔ 最佳答案
Refer to the figure below.

====
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

====
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

====
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
2020-06-22 11:49 am
(1/2) * 2 * 2 - (1/2) * 1 * 1 - 2 * 1 + (1/2) * pi * 1^2 - (1/2) * (1/2) * 1 + (1/2) * (3/2) * 3 + 1 * 3 =>
(1/2) * 4 - (1/2) * 1 - 2 + pi/2 - (1/4) + (3/4) * 3 + 3 =>
2 - (1/2) - 2 + (pi/2) + (9/4) - (1/4) + 3 =>
(-1/2) + (pi/2) + (8/4) + 3 =>
(pi - 1) / 2 + 2 + 3 =>
5 + (pi - 1) / 2 =>
(10 + pi - 1) / 2 =>
(9 + pi) / 2


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