A- Find the Riemann sum for f(x) = 7 sin x, 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Round your...

Hello!

Summands of the Riemann sum have a form

`Delta x_n*f(x_n),`

where segments `d_n` of length `Delta x_n` cover the integration segment and each `x_n` is in `d_n.`

In our problem all length of subintervals are considered equal, i.e.

`Delta x = Delta x_n = ((3pi)/2)/6=pi/4.`

`x_n`'s are right endpoints, the formula for them is obviously

`x_n=n*pi/4,`  `n` is from 1 to 6.

So the sum is  `pi/4 sum_(n=1)^6 (7sin(n*pi/4)).`

All terms are known, and this sum is equal to

`(7pi)/4 (sqrt(2)/2+1+sqrt(2)/2+0+(-sqrt(2)/2)+(-1)) = (7sqrt(2))/8 pi.`

The approximate value is 3.887523.