Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. M4 = ? I got the...

The midpoint rule basically estimates the area under a
curve by sampling it a n-1 points, and using the rectangle with height f(Xn) and width
(b-a)/n at each point to give the area under that portion of the
curve.

So,

f(x) = 3x^3 e^-2x ,
 x = [1,5]

dx = 5-1 / 4 =
1

The first point is the midpoint between a and a + dx : a
+ dx/2, or 1.5. Each point after that is spaced at dx =
1.

f(1.5) = 0.68

f(2.5)
= 5.29

f(3.5) = 20.3

f(4.5)
= 55.5

So,

Int( f(x) ) , x =
[1,5] ~~ dx*(0.68 + 5.29 + 20.3 + 55.5) =
81.77

You can compare this with the exact
answer,

3124/(5 e^2) ~~ 84.5575