If int_(0)^(x)f(t)dt=x+int_(x)^(1)tf(t)dt , then the value of f(1) is View Solution Let f(x)=∫x0costtdt,(x>0),then for x = (2n+1)π2f(x) has View Solution Exams IIT JEE NEET UP Board Bihar Board CBSE
dt , f(x+π) View Solution f(x)=sinx+∫π/2−π/2(sinx+tcosx)f(t) dt then max value of f (x) : View Solution Exams IIT JEE NEET UP Board Bihar Board CBSE Free Textbook Solutions KC Sinha Solutions for Maths Cengage Solutions for Maths ...
进行求导运算的结果是什么? 二、解析 令u = x − t,则: t=x–u. dt=–du. 又由于 t ∈ (0,x), 因此,u = x − t ∈ (x,0). Next 于是: ∫0xtf(x–t)dt= –∫x0(x–u)f(u)du= ∫0x(x–u)f(u)du= ∫0xx⋅f(u)du–∫0xu⋅f(u)du= x∫0xf(u)du–∫0xu...
【解析】令u=x-t,原方程化为: f(dt=z+(u)du-; 。u时(u 两边对x求导,得f(x)=1+f(u)du+f() ①; -rf()=1+f(u)du… 两边再对x求导,得f(x)=f(x); 解得nf(x)|=x+n|C,即f(x)=Ce2; 将x=0代入①,得f(0)=1; f(0)=Ce°=1,解得C=1; ∴f(x)=e2.相...
【解析】33.【精析】等式 ∫_0^xtf(t)dt=x^2+f(x) 两端对x求导得xf(x)=2x+f'(x) ,即 f'(x)=xf(x)=-2x记y=f(x),则 y'-xy=-2x ,此为一阶线性微分方程,通解为y=e^(-∫2(x)dx)[∫Q(x)dx+C]=2+Ce^(1/2x^2)等式 ∫_0^xtf(t)dt=x^2+f(x) 中,令x...
Answer and Explanation: {eq}g(x) = \begin{cases} \int_0^x 0 \, dt & \text{if} & t < 0\ \int_0^x \,t \, dt & \text{if} & 0 \leq t \leq 1\ \int_0^x (2 - t) \, dt &.....
यदि `g(x) = int_(0)^(x) f(t)dt` जबकि `1... यदिg(x)=∫x0f(t)dtजबकि12≤f(t)≤1,t∈[0,1]तथा0≤f(t)≤12,t∈[1,2]के लिये, तब g(2) A
Answer Step by step video & image solution for int_0^x f(t)dt=x+int_x^1 tf(t)dt হলে f(1) এর মান নির্ণয় করো। by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams.Updated on:21/07/2023 ...
1.求下列函数的导数:(1) f(x)=∫_1^x(t+sint^3)dt ;(2) f(x)=∫_1^(x^2)ln^3dt Int3dt;.0(3) f(x)=∫_x^0e^(-t^2)dt ;x(4)f(x)=∫_(x^2)^(x^3)1/(√(1+t^4))dt. 相关知识点: 试题来源: 解析 1. (1)x+sinx^3 ; (2)2xlnx^6 ; (3)-...
高等数学 积分函数的奇偶性的一个问题,求指点若f(x)是奇函数,则 $$ \int _ { 0 } ^ { x } $$f(t)dt为偶函数;若f(x)是偶函数,则 $$ \int _ { 0 } ^ { x } $$f(t)dt为奇函数.&偶函数的原函数之一为奇函数“导函数为奇函数,那么原函数为偶函数;导函数为偶函数,那么...