<html><body><div style="color:#000; background-color:#fff; font-family:arial, helvetica, sans-serif;font-size:10pt"><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><span>Tiago,</span></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><span><br></span></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><span>Se for possível calcular o valor da função em qualquer ponto, então talvez você possa utilizar integração por Monte Carlo. Por exemplo:</span></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><span><br></span></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><span><br></span></div><div><span style="font-size: 13px; "><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "># Cálculo de volume (1/8 de esfera de raio r)</div><div style="font-family: 'Courier New', courier, monaco,
monospace, sans-serif; ">r<-1</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">ux<-runif(2e4,0,r)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">uy<-runif(2e4,0,r)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">uz<-runif(2e4,0,r)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">id<-ux^2+uy^2+uz^2<=r^2</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">mean(id)*r^3 # Aproximado</div><div style="font-family: 'Courier New', courier, monaco, monospace,
sans-serif; ">4*pi*r^3/(3*8) # Exato</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "># Vizualização</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">np=200</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">x<-seq(0,r,l=np)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">z<-outer(x,x,function(x,y) sqrt(r^2-x^2-y^2))</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">library(rgl)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif;
">persp3d(x,x,z)</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; ">points3d(ux,uy,uz,pch=20,col=ifelse(id==TRUE,4,2))</div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div style="font-family: 'Courier New', courier, monaco, monospace, sans-serif; "><br></div><div>Att.,</div><div>Rubem</div></span></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><br></div><div style="font-size: 10pt; font-family: arial, helvetica, sans-serif; "><div style="font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; "><br> </div> </div> </div></body></html>