p 级数顺序零点右导数设f(x)在区间[0,a]上可积,在[0,a]上连续,且有无限多个零点 x_i(i=1,2,3,…):a≥x_1x_2…x_mx_(n+1)…0,■(x_n-x_(n+1))/x_n=0;■■f(t)dt 则 F■(0)=0.doi:CNKI:SUN:FGJK.0.1993-04-019眭润生无锡轻工业学院纺织分院基础部CNKI纺织高校基础科学学报...
容易被忽略的隐含条件.用分析的方法,通过定义一个定积分的变上限函数,可证明变上限函数F(x)=integral from n=0 to x((x-t)~nf(t)dt)必须满足的n+1个... 王良成,白海 - 《高等数学研究》 被引量: 0发表: 2009年 一道高等数学习题的四种证法 In this paper ,assuming f (x) is contin...
(t)的定积分integral from n=0 to T(f(t)dt)可以近似地用sum from i=1 to n(fi*t)来表示,其中n为周期T内的采样点数,n必须足够大,fi为t=i*△t... 苏丽萍,刘全海 - 《机械职业教育》 被引量: 2发表: 1997年 一类抛物型方程的系数反演问题 t)dt)~2+2Z_(Tx)(x)/Z_T(x)integral from n=...
广义积分∫0^1(ln^k―1t/1+t)dt与级数Σn=1→∞(―1)^n―1/n^k间的关系及计算 摘要: 吴天毅 被引量: 0发表: 0年 Bernoulli数与广义积分integral from n=0 to (+∞){〔x^(k-1)〕/〔e^x±1〕}dx的精确表示 本文利用Bernoulli数,获得了两类重要广义积分integral from n=0 to(+∞){〔...
∫sec3(x)tan(x)dx Evaluating the Integral of Product of Trigonometric Functions: To simplify the given trigonometric integrand, we need to rewrite the product of trigonometric functions using the general multiplication rule,a3=a×a×a. Then, we either have to apply trigonometric identities...
函数integral from n=a to x(f(t)dt)的可导性探讨 设有界函数f(x)在(a,b)上Riemann可积,对f(x)的不连续点,Φ(x)=integral from n=a to x(t)dt的可导性如何呢?本文指出:设X 0 是f(x)在(a,b)上的不连续点,f(x)在(a,b)上... 王家炳,宋天鉴 - 《曲靖师范学院学报》 被引量...
\int_0^{\infty} e^{5x}dx Determine whether the following integral is convergent or not. You need to justify it (prove it). If it is convergent, find its value. \int\frac{\sin (x^2)}{x^2}dx Determine whether the integral is convergent or convergent. Evaluate, if ...
What is the integral of x2 from x=0 to 1? The Fundamental Theorem of Calculus: The fundamental theorem of calculus is an extremely important theorem in the area of integrals within the study of calculus. this is because it gives us a formula that we can use to calculate definite integrals...
The substitution of some variable in the place of trigonometric ratios is known as the trigonometric substitution. We will use the trigonometric integral to evaluate the integral of the given function. Answer and Explanation:1 Given: I=∫cot(x)dxI=∫cos(x)sin(x)dx ...
The value of ∫|x|0{x} dx (where [⋅] and {⋅} denotes greatest integer and fraction part function respectively) is A12[x] B2[x] C12[x] D[x]Submit The value of the integral ∫10{4t3(1+t)8+8t4(1+t)7}dt is A128 B512 C256 D1024Submit The value of the integral ⇒...