# Solve an Equation Including Integral Classic List Threaded 4 messages Open this post in threaded view
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## Solve an Equation Including Integral

 Dear All: I submitted this post to the R-sig-Teaching List too I am trying to solve an equation including an integral for unknown parameter. Is this can be done in R? if so, any helps will be highly appreciated ### The following function is a function of t, given exi, nu, and alpha. fun<-function(exi,nu,alpha) (nu+t^2)^(-(nu+1)/2)*exp(((nu+1)*exi*t)/((nu+t^2)^0.5)) ### I want to solve "[Integral(-Inf,100) fun(exi,nu,alpha)]-(1-alpha)=0" for t. ### That is, find the value of t which satisfy the equation:              [Integral(-Inf,100) fun(exi,nu,alpha)]-(1-alpha)=0 ### for example given: alpha = 0.05, nu = 20 , exi = 0.5, Solve for t. with many thanks steve -------------------------- Steven M. Stoline 1123 Forest Avenue Portland, ME 04112 [hidden email]         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Solve an equation including integral

 I think this is what you want: myroot <- function(t, nu, exi, alpha){   fun <- function(t, exi, nu) (nu+t^2)^(-(nu+1)/2)*exp(((nu+1)*exi*t)/((nu+t^2)^0.5))   res <- alpha - integrate(fun, -Inf, t, nu=2, exi=0.5)\$value   return(res) } uniroot(myroot, c(-2, 2), nu=2, exi=0.5, alpha=.05) Hope this is helpful, Ravi Ravi Varadhan, Ph.D. (Biostatistics), Ph.D. (Environmental Engg) Associate Professor,  Department of Oncology Division of Biostatistics & Bionformatics Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University 550 N. Broadway, Suite 1111-E Baltimore, MD 21205 410-502-2619         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.