Answer Happy

Definition: The AREA A of the region S that lies under the graphof the continuous function f is the limit of the sum of the areasof approximating rectangles
A=limn→∞Rn=limn→∞[f(x1)Δx+f(x2)Δx+...+f(xn)Δx]A=limn→∞Rn=limn→∞[f(x1)Δx+f(x2)Δx+...+f(xn)Δx]
Consider thefunction f(x)=ln(x)x,3≤x≤10.f(x)=ln⁡(x)x,3≤x≤10. Usingthe above definition, determine which of the following expressionsrepresents the area under the graph of ff as a limit.
Definition: The AREAA of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A=n→∞lim​Rn​=n→∞lim​[f(x1​)Δx+f(x2​)Δx+…+f(xn​)Δx] Consider the function f(x)=xln(x)​,3≤x≤10. Using the above definition, determine which of the following expressions represents the area under the graph of f as a limit. A. n→∞lim​i=1∑n​n10​n10i​ln(n10i​)​ B. n→∞lim​i=1∑n​n7​3+n7i​ln(3+n7i​)​ C. n→∞lim​i=1∑n​n7​n7i​ln(n7i​)​ D. n→∞lim​i=1∑n​n10​3+n10i​ln(3+n10i​)​ E. n→∞lim​i=1∑n​3+n7i​ln(3+n7i​)​