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PinkyPYC一星新手會員
2011-4-9 17:24#1
1. Evaluate the following indefinite integrals:
(a) ∫ (1− x) x^1/2 dx
(b) ∫ 8x^3−6x^2−ex^4 / 3x^3 dx
(c) ∫ 3x (1− 2x^2)^1/2 dx
(d) ∫ (x+3) / (x^2+6x)^1/3 dx
(e) ∫ dx / 2x − 3
2. A lighthouse is at a point A, 5km offshore from the nearest point O of a
straight beach; a store is at point B, 6km down the beach from O. If the
lighthouse keeper can row 2km/h and walk 4km/h, how should she
proceed in order to get from the lighthouse to the store in the least
possible time?
3. Find the indefinite integral of each of the following:
(a) ∫ e^x^1/2 / x^1/2 dx
(b) ∫ x^2 (x^3+2)^1/2 dx
(c) ∫ 3x^2 / (x^3+10)^3 dx
(d) ∫ (e^x+1)^7 e^x dx
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36661124二轉會員
2011-4-13 07:33#2
咁多-,-?
HINT ONLY:
(a) ∫ (1− x) x^1/2 dx
EXPAND (1− x) x^1/2 -> x^1/2 - X^3/2
b) in ex^4 / 3x^3 dx = in ex dx = e [in x dx ] e is a constant
c) let (1− 2x^2) = y -4xdx=dy
d)let (x^2+6x)^1/3 = y
e) let 2x-3 =y , 2dx=dy
3a) let x^1/2=y => (0.5) x^-1/2dx=dy =>[0.5/x^1/2 ]dx=dy
b)let (x^3+2)^1/2 =y
c: let(x^3+10)^3 =y
d) (e^x+1)^7 e^x =(e^x+1)^7( e^x +1 -1) =(e^x+1)^8 - (e^x +1)^7 ,then let e^x +1 =y
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PinkyPYC一星新手會員
2011-4-18 23:05#3
可否請清楚係點做呀？
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36661124二轉會員
2011-4-19 16:28#4
你想清楚成點?
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PinkyPYC一星新手會員
2011-4-19 23:12#5
講解一下點解係咁樣計
因為以前未學過，依家學極都唔明唔識
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36661124二轉會員
2011-4-19 23:32#6
你認清返最基本既integration先
ie : in x dx = x^2 /2 + c
如果題目: in (x+10)^2 dx
咁你沒學過in (x+10) ^2 dx e個野,咪唯有將中間果舊野爆開佢 ,變到 in x^2 + 20x +100 dx =[ in x^2 dx + in 20x dx + in 100 dx]<<e 揪野你識in
[ 本帖最後由 36661124 於 11-4-19 11:33 PM 編輯 ]
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雪子秀版主
2011-4-20 14:42#7
原帖由 36661124 於 19/4/2011 11:32 PM 發表 
你認清返最基本既integration先
ie : in x dx = x^2 /2 + c
如果題目: in (x+10)^2 dx
咁你沒學過in (x+10) ^2 dx e個野,咪唯有將中間果舊野爆開佢 ,變到 in x^2 + 20x +100 dx =[ in x^2 dx + in 20 ...
不如開"小畫家"來做更加清晰。:smilie_:o:
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PinkyPYC一星新手會員
2011-4-21 22:54#8
我都覺得應該會清楚易明d
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abcdefg111一星新手會員
2011-4-22 00:44#9
36661124兄 講既野
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雪子秀版主
2011-4-22 11:52#10
原帖由 abcdefg111 於 22/4/2011 12:44 AM 發表
36661124兄 講既野
好似少了 + C。
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PinkyPYC一星新手會員
2011-4-22 22:51#11
好似好複雜咁...:smilie_:(:
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NaozumiVIP會員
2011-4-23 11:47#12
原帖由 雪子秀 於 11-4-22 11:52 發表
好似少了 + C。
只要keep番住個indefinite integral (右邊)都唔洗 +C
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NaozumiVIP會員
2011-4-23 11:48#13
原帖由 PinkyPYC 於 11-4-22 22:51 發表
好似好複雜咁...:smilie_:(:
呢d只係以前中五課程,其實只係好機械咁用公式, 呢d冇shortcut走,只有用到熟
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PinkyPYC一星新手會員
2011-4-23 22:05#14
但慘在我中五只係齋讀maths，冇讀呢丁野...:smilie_:(:
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NaozumiVIP會員
2011-4-24 12:27#15
冇緊要啦,咪重頭學過, 就算出黎做野都係要學野
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PinkyPYC一星新手會員
2011-4-24 18:06#16
係要學過但每課上完一兩堂就要交功課
想學得識都幾困難...
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36661124二轉會員
2011-4-26 23:43#17
原帖由 PinkyPYC 於 11-4-24 06:06 PM 發表
係要學過但每課上完一兩堂就要交功課
想學得識都幾困難...
IN 同D 自學其實都沒咩問題
最重要係睇熟書D EXAMPLE
狂做狂做!
當然預習係好重要!
果時我都係自己預習IN同D,
睇住書d example ,睇下d 同in果時有咩skills
你就學左佢
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PinkyPYC一星新手會員
2011-4-27 22:47#18
明白晒...
但我仲係唔係好識點做