3. -6 points SCalcCC4 59 002 The left, right, Trapezoidal, and Midpoint Rule app

Question

3. -6 points SCalcCC4 59 002 The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate the following where f is the function whose graph is shown below it. f (r) dr The estimates were 0.7819, 0.8631, 0.86795, and 0.9540, and the same number of subintervals were used in each case. (a) Which rule produced which estimate? ·P-Select M Select (b) Between which two approximations does the true value of the integral lie? Select- (best under-estimate) select-v1 (best upper-estimate) Need Help?Ree Tak to Teter 4. -3 points SCalcCC4 5 9 007 MI O Type here to search

Explanation / Answer

Right
Trpzdal
Left
Midpt

This is a continuously decreasing function

So, the left end sum is an overestimate
And right end sum is an underestimate

So, left end sum = 0.9540

Right end sum = 0.7819

Now, between mp and trpzdal , since the function is concave up,
the trpzdal rule is an overestimate and thus will be the larger value

Thus ,trpzdal rule = 0.86795

And midpoint rule = 0.8631

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b)
The true value lies always between right and left end sums

So, between
0.7819
and
0.9540

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