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標題:

Maclaurin Series 1

• 1987年8月31日上午10-00出世既女仔係點的--@1@
• 尖鼻咀去白泥的交通@1@
• ”記錄”與”紀錄”文法上之分別@1@

• 1987年8月31日上午10-00出世既女仔係點的--@1@
• 尖鼻咀去白泥的交通@1@
• ”記錄”與”紀錄”文法上之分別@1@

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發問:

Using the part of the Maclaurin series of cos x = 1 - x^2/2! + x^4/4! - x^6/6! + ... up to only the second term, i.e., the x^2 term, an approximate value of the integral√x cos(x^2)dx: [asnwer: 19/33] Detail: http://postimg.org/image/y11c4clin/

最佳解答:

cos x = 1 - x^2/2! cos(x^2) = 1 - x^4/2! sqrt x cos(x^2) = x^(1/2)[ 1 - x^4/2!] = x^(1/2) - x^(9/2)/2! ∫ sqrt x cos(x^2) dx = ∫ x^(1/2) - x^(9/2)/2! dx = 2x^(3/2)/3 - x^(11/2)/11 when x = 0 the integral = 0 when x = 1, the integral = 2/3 - 1/11 = (22 - 3)/33 = 19/33.

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