Let 

?
Use a Riemann sum with four subintervals of equal length  to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals.
?
__________ sq units
?
Repeat previous part with eight subintervals of equal length .
?
__________ sq units
?
Compare the approximations obtained in previous parts with the exact area (12 sq units). Do the approximations improve with larger n?

What will be an ideal response?


14.4; 13.2; yes

Mathematics

You might also like to view...

Find the volume of the indicated region by an iterated integration.The region bounded by the surface  , the cylinder  , and the 

A. ?
B. 5000?
C. ?
D. 2500?

Mathematics

Solve the problem.The position of a body moving on a coordinate line is given by  with s in meters and t in seconds. When, if ever, during the interval  does the body change direction?

A. t = 3.5 sec B. t = 7 sec C. no change in direction D. t = 14 sec

Mathematics

Graph the function.f(x) = 2- x - 4

A.

B.

C.

D.

Mathematics

The following table shows the earnings for the Juarez family last year. Use this information to answer the question.MonthEarningsMonthEarningsJan.$1400July$1300Feb.$1150Aug.$2450Mar.$2950Sept.$2500Apr.$2300Oct.$2000May$1650Nov.$2350June$2700Dec.$2400What was the family's total income from January thru June?

A. $11,000 B. $9,200 C. $12,150 D. $13,000

Mathematics