Use the midpoint rule with n = 5 to estimate the volume v obtained by rotating about the y-axis the region under the curve y = 1 + 9x3 , 0 ≤ x ≤ 1. (round your answer to two decimal places.)

Using the shell method, the volume is given exactly by the definite integral,

Splitting up the interval [0, 1] into 5 subintervals gives the partition,

[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]

with left and right endpoints, respectively, for the -th subinterval

where . The midpoint of each subinterval is

Then the Riemann sum approximating the integral above is

(compare to the actual value of the integral of about 14.45)

what are the statements

step-by-step explanation:

529 and 531

step-by-step explanation: