Use the Midpoint Rule with the given value of n to approximate the integral. Use the Midpoint Rule with the given value of n to approximate the integral.   Integral 0 to (pi/2) 2cos^(5)x dx , n=4 M4=__________________?

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You should evaluate the integral using midpoint rule, hence, you need to split the interval `[0,pi/2]`  in n = 4 subintervals of equal width such that:

`[0 , pi/8] , [pi/8 , pi/4] , [pi/4 , 3pi/8] , [3pi/8 , pi/2]`

You need to find the midpoint of each subinterval such that:

`x_1 = (pi/8 - 0)/2 , x_2 = (pi/4 - pi/8)/2 , x_3 = (3pi/8 - pi/4)/2 , x_4 = (pi/2 - 3pi/8)/2`

Evaluating the integral using the midpoint rule, yields:

`int_0^(pi/2) 2 cos^5 x dx =...

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