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Rewriting a $maxleft0,dotsright$ function in order to integrate the function more properly

Finding an inverse Laplace transform of an integral that involves the $maxleft0,dotsright$ functionIntegral $int_0^infty x^2,e^-x^2operatornameerf(x),log(x),dx$Closed form for $largeint_0^1fracln^3xsqrtx^2-x+1dx$Closed form of the integral $largeint_0^infty e^-xprod_n=1^inftyleft(1-e^-24!;n!;xright)dx$Undo a convolution involving an inverse Laplace transform and definite integralEvaluating the closed form for $int_0^inftyln^kleft(1+1over xright) cdotmathrm dxover (1+x)^n=F(k,n)$Find an integral involving the exponential function with iAn approximation of the real part of $int_0^pi/2xleft(-1+sin xright)^log x dx$Proving that a double integral convergesProving that a solution to a differential equation is monotonicFinding an inverse Laplace transform of an integral that involves the $maxleft0,dotsright$ function

0

$begingroup$

Yesterday I asked a question about a certain integral. In the integral is the term:

$$maxlefttextncdotsinleft(2picdot xcdot t-fracpi2right)righttag1$$

I know that $x$, $textz$ and $textn$ are all real and positive numbers.

Next to that I know that the integral is between certain boundaries (where only the lower bound is important for the function that I stated in equation $(1)$). I know that:

$$frac14xle t<frac12xtag2$$

Question: is there a way to rewrite equation $(1)$ using the condition that is stated in equation $(2)$ so that I lose the $maxleft0,dotsright$ function? If that is possible I can use that to evalute the integral using Mathematica more easily.

calculus functional-analysis definite-integrals absolute-value maxima-minima

share|cite|improve this question

asked Mar 20 at 18:31

JanJan

22k31440

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  the function $max(0,x)$ can be written $(|x|+x)/2$, does that help?
  $endgroup$
  – Calvin Khor
  Mar 20 at 18:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @CalvinKhor Where does that relation come from? I've never seen that.
  $endgroup$
  – Jan
  Mar 20 at 18:58
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  well, when $xge 0$, then $|x|=x$, and when $x<0$, $|x|=-x$.
  $endgroup$
  – Calvin Khor
  Mar 20 at 18:59
  

  
  
  
  

add a comment | 

0

$begingroup$

Yesterday I asked a question about a certain integral. In the integral is the term:

$$maxlefttextncdotsinleft(2picdot xcdot t-fracpi2right)righttag1$$

I know that $x$, $textz$ and $textn$ are all real and positive numbers.

Next to that I know that the integral is between certain boundaries (where only the lower bound is important for the function that I stated in equation $(1)$). I know that:

$$frac14xle t<frac12xtag2$$

Question: is there a way to rewrite equation $(1)$ using the condition that is stated in equation $(2)$ so that I lose the $maxleft0,dotsright$ function? If that is possible I can use that to evalute the integral using Mathematica more easily.

calculus functional-analysis definite-integrals absolute-value maxima-minima

share|cite|improve this question

asked Mar 20 at 18:31

JanJan

22k31440

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  the function $max(0,x)$ can be written $(|x|+x)/2$, does that help?
  $endgroup$
  – Calvin Khor
  Mar 20 at 18:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @CalvinKhor Where does that relation come from? I've never seen that.
  $endgroup$
  – Jan
  Mar 20 at 18:58
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  well, when $xge 0$, then $|x|=x$, and when $x<0$, $|x|=-x$.
  $endgroup$
  – Calvin Khor
  Mar 20 at 18:59
  

  
  
  
  

add a comment | 

$begingroup$

Yesterday I asked a question about a certain integral. In the integral is the term:

$$maxlefttextncdotsinleft(2picdot xcdot t-fracpi2right)righttag1$$

I know that $x$, $textz$ and $textn$ are all real and positive numbers.

Next to that I know that the integral is between certain boundaries (where only the lower bound is important for the function that I stated in equation $(1)$). I know that:

$$frac14xle t<frac12xtag2$$

Question: is there a way to rewrite equation $(1)$ using the condition that is stated in equation $(2)$ so that I lose the $maxleft0,dotsright$ function? If that is possible I can use that to evalute the integral using Mathematica more easily.

calculus functional-analysis definite-integrals absolute-value maxima-minima

share|cite|improve this question

asked Mar 20 at 18:31

JanJan

22k31440

$endgroup$

share|cite|improve this question

asked Mar 20 at 18:31

JanJan

22k31440

share|cite|improve this question

asked Mar 20 at 18:31

JanJan

22k31440

asked Mar 20 at 18:31

JanJan

22k31440

asked Mar 20 at 18:31

JanJan

22k31440