证明：我们视函数g为一个随机变量，将区间[a,b]任意分为n份，使得每一份区间长度小于任给出的正数ε>0a=x0<x1<x2<···<xn=b则g的期望可计算：Eg=∑k=0n−1g(xk)xk+1−xkb−a=1b−a∫abg(x)dx 证完。现在考虑本题：易知limn→∞∫0π2sinnxdx=limn→∞∫0π2cosnxdx 取s...
1) Use integration by parts to evaluate (a) \int x e^{-x} dx (b) \int x sin x dx (c) \int \frac{lnx}{x} (d) \int lnx dx 2) Use trigonometric substitution to evaluate (a) \int \frac{dx}{\sqrt {a^2 - x Evaluate the integral by p...
∫f(x)g(x)dx=f(x)∫g(x)dx−∫f′(x)(∫g(x)dx)dx. We recall the following formulas of given problem: ddx(xn)=nxn−1,∫sinaxdx=−cosaxa+c,∫cosaxdx=sinaxa+c, where c is a constant of integration. Answer and Explanation: Let I=∫x sin (x) ...
With a step of integration by parts we have I=∫102xarcsinx1−x4−−−−−√dx=π24−∫10arcsin(x2)1−x2−−−−−√dxI=∫012xarcsinx1−x4dx=π24−∫01arcsin(x2)1−x2dx which is extremely good in simplifying the hypergeometric structure: I=...
∫π0f∞(x)dx=∫π0−x+Sa(x)dx=∫π0−xdx+∫π0Sa(x)dx=−π22+(πSa(π)−0Sa(0)−∫Sa(π)Sa(0)y−sinydy)=−π22+(π2−∫π0y−sinydy)=−π22+(π2−[y22+cosy]π0)=2.∫0πf∞(x)dx=∫0π−x+Sa(x)dx=∫0π−xdx...
integration:"); scanf_s("%lf %lf", &a, &b); printf("Please enter specific calculation function(1-sin/2-cos/3-exp): "); scanf_s("%d", &func_idx); switch (func_idx) { case 1:printf("The integral of sin(x) is:%lf\n", integral(sin, a, b, n)); break; case 2:printf...
ist eine Stammfunktion von{\displaystyle {\frac {1}{\sin x}}} . {\displaystyle \int _{0}^{\frac {\pi }{2}}{\frac {x^{2}}{\sin x}}\,dx} ist damit nach partieller Integration {\displaystyle \underbrace {\left[x^{2}\,F(x)\right]_{0}^{\frac {\pi }{2}}} _{=0}-...
Evaluate the following integration int 2^(x)*e^(x)*dx 02:46 Evaluate: int(e^(3x)+e^(5x))/(e^x+e^(-x))dx 01:21 int (e^(xloga)+e^(alogx))dx 02:19 int(1+cos4x)/(cotx-tanx)\ dx 06:59 Evaluate : int tan x tan 2 x tan 3x dx 02:44 Evaluate the following integrat...
Inteqral for mulas of triangle integration ∫dx/sin~nx and ∫dx/cos~nx By means of separately partial integration formula and recurrence formula, we get the integration formulas of triangle integration ∫dxsin nx and ∫dxcos n... Q Wang 被引量: 0发表: 2001年 ...
Evaluate the following integrals: intcosx cos 2x cos3x dx 04:51 Evaluate the following integrals: int sin mx sin nx dx 03:40 Evaluate the following integrals: intsin mx cos nx dx where m and n ... 02:16 Evaluate the following integrals: intsin^3 x cos^3 x dx 03:00 Evaluate the...