વિધેય f(x)=int limits_0^2 e^{|x-t|} d t નું ન | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

For $x \leq 0$

$f(x)=\int \limits_0^2 e^{t-x} d t=e^{-x}\left(e^2-1\right)$

For $0 < x < 2$

$f(x)=\int \limits_0^x e^{x-t} d t+\int \li

Vedclass · Accepted Answer

$2(e-1)$

Vedclass · Answer

For $x \leq 0$

$f(x)=\int \limits_0^2 e^{t-x} d t=e^{-x}\left(e^2-1ight)$

For $0 < x < 2$

$f(x)=\int \limits_0^x e^{x-t} d t+\int \limits_x^2 e^{t-x} d t=e^x+e^{2-x}-2$

For $x \geq 2$

$f(x)=\int \limits_0^2 e^{x-t} d t=e^{x-2}\left(e^2-1ight)$

For $x \leq 0, f ( x )$ is $\downarrow$ and $x \geq 2, f ( x )$ is $\uparrow$

$	herefore$ Minimum value of $f ( x )$ lies in $x \in(0,2)$

Applying A.M $\geq$ $G.M$

minimum value of $f(x)$ is $2(e-1)$

વિધેય $f(x)=\int \limits_0^2 e^{|x-t|} d t$ નું ન્યૂનતમ મૂલ્ચ $.............$ છે.

Similar Questions

$\int_0^1 {\frac{{{x^b} - 1}}{{\log x}}} \,dx = . . . ..$

જો $\frac{d}{{dx}}\,G\left( x \right) = \frac{{{e^{\tan \,x}}}}{x},\,x \in \left( {0,\pi /2} \right)$, તો $\int\limits_{1/4}^{1/2} {\frac{2}{x}} .{e^{\tan \,\left( {\pi \,{x^2}} \right)}}dx$ મેળવો.

જો $\frac{d}{{dx}}F(x) = \left( {\frac{{{e^{\sin x}}}}{x}} \right)\,;\,x > 0$. અને $\int_{\,1}^{\,4} {\frac{3}{x}{e^{\sin {x^3}}}dx = F(k) - F(1)} $, તો $k$ ની કોઈ એક શક્ય કિમત મેળવો.

જો $\int\limits_0^1 {(1 + |\sin x|)(a{x^2} + bx + c)dx = \int\limits_0^2 {(1 + |\sin x|)(a{x^2} + bx + c)} } dx$

હોય તો સમીકરણ ${a{x^2} + bx + c}=0$ ના બીજ એ . . . .