a<-seq(70,90,0.1);
numIter=length(a);
answer=rep(0,numIter);

integrand <- function(theta) {
(theta - temp)^2 * dnorm(theta,77.33,1.07)
}
integrand3 <- function(theta) {
3 * (theta - temp)^2 * dnorm(theta,77.33,1.07)
}


for (i in 1:numIter) {
	temp <- a[i];
	answer[i] <- integrate(integrand3,lower=-Inf,upper=temp)$value+integrate(integrand,lower=temp,upper=Inf)$value
}

plot(a,answer);

cat(a[which.min(answer)],"\n");