I do not understand what question # 5 is asking. The answer to # 2 is 36 and the

Question

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?

Explanation / Answer

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.

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