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

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

i think it might be a but you might want a second opinion