Answer:
-20.41
Step-by-step explanation:
We are given that:
n = 4
a = 0 rad
b = 80 rad
f(x) = sin (x)
The length of each sub interval is given by:
[tex]\Delta x=\frac{b-a}{n}\\\Delta x=\frac{80-0}{4}\\\Delta x=20\ rad[/tex]
The ends of each sub interval is found by, starting at a = 0, and adding 20 rad. The sub intervals are:
(0, 20) (20, 40) (40, 60) (60, 80)
The midpoints of each sub interval are the average between the start and end point:
(10) (30) (50) (70).
According to the midpoint rule, with n =4.
[tex]\int\limits^{80}_0 {f(x)} \, dx =\Delta x*(f(x_1)+f(x_2)+f(x_3)+f(x_4))\\\int\limits^{80}_0 {sin(x)} \, dx =20*(sin(10)+sin(30)+sin(50)+sin(70))\\\int\limits^{80}_0 {sin(x)} \, dx =-20.41[/tex]
The approximate integral is -20.41
