Let f(x) = x2, and compute the riemann sum of f over the interval [5, 7], choosing the representative points to be the midpoints of the subintervals and using the following number of subintervals (n). (round your answers to two decimal places.)
(a) use two subintervals of equal length (n = ) use five subintervals of equal length (n = ) use ten subintervals of equal length (n = 10).

a) 72.5

b) 72.64

c) 72.66

Step-by-step explanation:

(a) 2 sub-intervals of equal length (width = 2/2 = 1) would have their mid point at x = 5.5 and x = 6.5.

So the sum over interval [5,7] is

30.25*1 + 42.35*1 = 72.5

(b) 5 sub-intervals of equal length (width = 2/5 = 0.4) would have their mid point at x = 5.2, 5.6, 6, 6.4, 6.8

So the sum over interval [5,7] is

27.04*0.4 + 31.36*0.4 + 36*0.4 + 40.96*0.4 + 46.25*0.4 = 72.64

(c) 10 sub-intervals of equal length (width = 2/10 = 0.2) would have their mid point at x = 5.1, 5.3, 5.5, 5.7, 5.9, 6.1, 6.3, 6.5, 6.7, 6.9

So the sum over interval [5,7] is

0.2 * (26.01 + 28.09+30.25 + 32.49 + 34.81 + 37.21 + 39.69 + 42.25 +44.89 + 47.61) = 72.66

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: