(a) estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (round your answers to four decimal places.)
(b) repeat part (a) using left endpoints

  first, we are going to define variables as the following: 

a = 0 
a = π/2 
n = 4 rectangles 

Δx = [ b - a ] / n >Δx = [ π/2 - 0 ] / 4 = π/8 

right endpoints : 
sum( seq( 4 cos(x) * π/8 , x , 0+π/8 , π/2 , π/8 ) ) = 3.163065 underestimate 

left endpoints: 
sum( seq( 4 cos(x) * π/8 , x , 0 , π/2-(π/8) , π/8 ) ) = 4.733861 overestimate 

the reason because the actual estimate by integral as the following: 
π/2 
∫ 4cos(x) dx = 4 
0