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2024年12月16日 · Example 34 Evaluate ∫_0^ (𝜋/2 ) log⁡sin⁡𝑥 𝑑𝑥 Let I1=∫_0^ (𝜋/2 ) 𝑙𝑜𝑔 (𝑠𝑖𝑛𝑥) 𝑑𝑥 ∴ I1=∫_0^ (𝜋/2) 𝑠𝑖𝑛 (𝜋/2−𝑥)𝑑𝑥 I1= ∫_0^ (𝜋/2) 𝑙𝑜𝑔 (cos⁡𝑥 )𝑑𝑥 Adding (1) and (2) i.e. (1) + (2) I1+ I1=∫_0^ (𝜋/2) 〖𝑙𝑜𝑔 (sin⁡𝑥 )𝑑𝑥+∫_0 ...

How to compute the following integral? $$\int\log (\sin x)\,dx$$ Motivation: Since $\log (\sin x)'=\cot x$, the antiderivative $\int\log (\sin x)\,dx$ has the nice property $F'' (x)=\cot x$.

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不定积分计算器 可以用分析整合的方法，计算出一个给定变量的函数的不定积分（原函数）。 它也可以画出函数和它的原函数的图像。 请注意，计算的不定积分属于一类函数F (x) C，其中C …

sin log要么是把结果预先存储在计算器rom里，要么是用 泰勒展开 转换成多项式计算. 确定定义域之后，可以用泰勒级数，不过泰勒级数在哪一点展开呢？ 方法二：预先计算出一些点，查表 …

By making the change of variable u=\pi -x you get that I=\int_0^\pi x \ln (\sin x)\:dx=\int_0^\pi (\pi-u) \ln (\sin u)\:du=\pi\int_0^\pi \ln (\sin u)\:du-I giving I=\frac {\pi}2\int_0^\pi \ln (\sin …

3 天之前 · The log sine function, also called the logsine function, is defined by S_n=int_0^pi [ln (sinx)]^ndx. (1) The first few cases are given by S_1 = -piln2 (2) S_2 = 1/ (12)pi^3+pi (ln2)^2 …

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2014年12月16日 · log(sin(x)) = − log(2) − ∞ ∑ k = 1cos(2kx) k. Notice that an is not so difficult to compute, if one performs a round of integration by parts, bringing the logarithm into a …