माना f: (0,oo)to R निम्न के द्वारा f(x) =int(1/x)^xe^(-(t+1/t))dt/tपरिभाषित है | तब,
解: \int _{0}^{x}[ \int _{0}^{t}f(u)du]dt= \int _{0}^{x}f(t)(x-t)dt =[t \bullet \int _{0}^{t}f(u)du] \mid _{0}^{x}- \int _{0}^{x}tf(t)dt =x \cdot \int _{0}^{x}f(u)du- \int _{0}^{x}tf(t)dt =x \cdot \int _{...
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)-...
f(x)=∫π0f(t)dt=x+∫1xtf(t)dt, then the value of f(1) is 12 View Solution If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is View Solution If ∫x0f(t)dt=x2−∫x20f(t)tdt then find f(1). View Solution If int_(0)^(x...
Let {eq}g\left( x \right) = \int\limits_0^x {f\left( t \right)dt} {/eq}, where {eq}f {/eq} is the function whose graph is shown. Does the function {eq}g\left( x \right) {/eq} have any critical points? Critical P...
Given that, {eq}\frac {d}{dx}\int^{x^2}_0\frac {t \ dt}{t+15} {/eq} Now, {eq}\int^{x^2}_0 \dfrac{d}{dx} \dfrac{t \ dt}{t+15} + \dfrac{d}{dx}x^2...Become a member and unlock all Study Answers Start today. Try it now Create an acc...
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...
{ x } f ( t ) d t $$,x ∈[a,b],证明 (1)F(x)在[a,b]上连续; (2)F(x)在[a,b]上可导,且$$ F ^ { \prime } ( x ) = f ( x ) $$ 【解析】证明:(1)根据f(x)在[a,b]上是连续函 数,则∃$$ M > 0 \forall x \in \left[ a , b \right] ...
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 ...
Answer Step by step video, text & image solution for The value of lim_(xrarr0)(1)/(x^(3))int_(x)^(0) (tln(1+t))/(t^(4)+4) dt is by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams.Updated on:21/07/2023 ...