Problem 2: Estimate the area under the graph of f(x) = 4 cos(x) from x = 0 to x = π/2. (Round the answer to four decimal places.)(a) Use four approximating rectangles and right endpoints.
My work and answer (which is wrong according to the site)
Delta x= Pi/2 / 4 = pi/8
R4= pi/8 (3.8+3.4+2.5+1.6)
R4= 4.4375
(b) b) Use four approximating rectangles and left endpoints.
L4= pi/8 f(pi/8) + pi/8 f(pi/4) +pi/8 f(3pi/4)
L4= pi/8 (4 + 3.9 +3.3 + 2.7)
L4=5.4585
I made a graph so these values are my estimates
Thanks for your replies. So which values do I multiply the values you gave me by? so it's Pi/8 ( f(pi/8)+f(pi/4)+...)and so on. I'm lost on how to find the values needed (as you saw from 3.8 you bolded. Do I make graphs? Really confused on that.
6. Enough said
Thank you! I got 3.1631 as the R4 value.
From the left, how would the values change?
It would still be pi/8 (f(pi/8) + f (pi/4) + f(p(3pi/8) + f(pi/2)) and I know from the left side sum it is an over-estimation as compared to the under-estimation from the right.
thanks again for all of your help.