Question

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. INT from 0 to pi/2 (2cos5 x) dx, n = 4

Answer 1

Answer:

$M_4=0.4722$

Step-by-step explanation:

we are given integral as

$\int _0^{\frac{\pi }{2}}\left(2cos\left(5x\right)\right)dx\:$

n=4

Firstly, we will find delta x

$\Delta x=\frac{\frac{\pi}{2}-0 }{4}$

$\Delta x=\frac{\pi}{8}$

now, we can find mid-point sum

$M_4=(0.3925) \times( f((0+0.3925)/2)) + f((0.3925+0.785)/2)) + f((0.785+1.1775)/2)) + f((1.1775+1.57)/2)) )$

$M_4=(0.3925) * ( 1.1119679802993 + -1.960985790784 + 0.3852980309352 + 1.6668002599015 )$

$M_4=0.4722$