I do not understand what question 5 is asking The answer to

I do not understand what question # 5 is asking. The answer to # 2 is 36 and the answer to # 4 is 81/4. I need help with question 5 please

2) Estimate the area under the curve -x3 , from x-0 to x-4, by using left endpoints and n 4 2) Estimate the area under the curve = x. from x=0 to x=4, by using left endpoints and n 4 3) Express the integral below as the limit as n approaches infinity of a Riemann Sum . x3 dx 0 4) Simplify your answer as much as possible and then evaluate the limit ) Simplify your answ 5) Consider your answers to number 2 and your answer to number 4. Is the sum in 2 an \"over estimate, an \"under estimate\" or \"exactly the area\" under the curve? Is this limit from part 4 an \"overestimate\" an \"underestimate\" of the area, or is it the exact area under the curve in question?

Solution

In General, for an increasing function, Let hand sums under estimate and Right hand has over estimate.

Similarly, If a function is monotonic and increasing, the left-hand Riemann Sum is an underestimate and the right-hand Riemann Sum is an overestimate

Here the function f(x)=x^3 is increasing in the interval [0,4] on the Left hand sum. Then it is under estimate.