integrate sec 2 x

【益智】 傳說是小學1年級的數學題 好難~

9月 27, 2012

何憶青

kuso

How to Integrate Sqrt(1 + x^2) and Sqrt(a^2 + x^2) 這是在網路上看到的，據說這是大陸小學一年級的數學題，你知道答案是多少嗎？       解答：答案為2分析：圓為在外面算0，在裡面算-1；正方形在裡面算1，在外面算4；三角形在裡面算2，在外面算3。知道這些之後把裡外相加就行了，三角形（外）+圓（內）=2不過跳跳虎還有看The first step in integrating sqrt(1 + x^2) is to make the trigonometric substitution x = tan(u) and dx = sec(u)^2 du. Then the integral of sqrt(x^2 + 1) becomes ∫ sqrt(x^2 + 1) dx = ∫ sqrt(tan(u)^2 + 1) * sec(u)^2 du = ∫ sqrt(sec(u)^2) * sec(u)^2 du = ∫ ...

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亂馬的煩惱，變回男兒身時....

9月 27, 2012

何樂芹

kuso

integration - Integrate $\sqrt{x^2 - 2x}$ - Mathematics Stack ExchangeIn hopes of taking advantage of the identity $$\tan^2\theta=\sec^2\theta-1,$$ make the substitution: $$x-1=\sec\theta, \quad dx=\sec\theta\,\tan\theta\,d\theta.$$ Then we have $$ \int \sqrt{(...

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由兇殺案測試你的弱點

9月 27, 2012

郭憶香

kuso

How to Integrate Tan^2(x) and Tan^3(x), Tangent Squared and Cubed 題目：在一個兇殺案現場，你是一們偵探，被謀害的是一位年輕女子，比較特別的是，遇害時女子手中抓著一條斷裂的口紅，請用直覺推斷她遇害的原因。1.強盜闖入家中劫財劫色2.男友報復他移情別戀3.暗戀他的變態狂形為4.情敵下的毒手           &nbTo integrate the function tan^2(x), we apply the first key identity. This transforms our integral into ∫ tan^2(x) dx = ∫ [sec^2(x) - 1] dx = [ ∫ sec^2(x) dx ] - [ ∫ 1 dx ] = -x + ∫ sec^2(x) dx Since the derivative of tan(x) is sec^2(x), it implies that th...

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不用健身就能擁有六塊腹肌 讚啦~

9月 27, 2012

葉紫蕊

kuso

How to Integrate [1/(x^2 + 1)] dx? | Physics Forums - The Fusion of Science and Community男孩請快下單 女孩請買給你男朋友吧XD OK, as you asked for it: FIRST u = x^2 + 1, du/dx = 2x, du/2x = dx [tex]\int\frac{1}{x^2+1} \ dx = \int\frac{1}{u} \ \frac{du}{2x}[/tex] I can not do further because the x variable is still exist. SECOND [tex]x = tan \ \...

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殘酷的事實...

9月 27, 2012

彭香珍

kuso

Integrate e^x(1-e^2x)^(1/2)dx - Math Help Forumwell......有些事情還是不要知道的好-.- Hi, I was wondering if you guys could check my work for indefinite integral of (e^x)(sqrt{1-e^2x) Let u=e^x The integral becomes: integral of sqrt(1-u^2) Then I do trigonometric substitution where I let u=sinx, and I get: 1/2 sin^-1(x) + (x/2)*(1 - x^2)^1...

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【可愛】龍貓大餐~

9月 27, 2012

郭靖萍

kuso

How do I integrate tan^2(x)? - YouTubeso~cute !!! In this video, I demonstrate how to find the anti-derivative or the integral of tan^2(x). This would normally be quite a difficult integral to solve. However, the ever powerful trigonometric identities make this an easy problem. By realising that tan^2(x)...

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