Question

Anyone pls help me check my answer

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.
f(x) = cos(x), [0, π/2], 4 rectangles

use left endpoints
http://www.wolframalpha.com/input/?i=Sum%5Bcos%28pi%2F8%29*%28i-1%29*%28pi%2F8%29%2C+%7Bi%2C+4%7D%5D

use right endpoints
http://www.wolframalpha.com/input/?i=Sum%5Bcos%28pi%2F8%29i*%28pi%2F8%29%2C+%7Bi%2C+4%7D%5D

Answer 1

for left hand evaluation,
\[
x_k=kh,\qquad k=0,1,2,3,\ldots
\]

Answer 2

and since you are using Wolfram, it is not YOUR answer, it is Wolfram's and he is correct with a very high degree of accuracy

Answer 3

the only problem is, you have to tell him the correct thing to solve

Answer 4

where\[h=\Large\frac{\pi/2}{4}={\pi\over8}\]
and you are evaluating
\[
\sum_{k=0}^3\cos(x_k)=\sum_{k=0}^3\cos\left(\pi k\over 8\right)
\]

Answer 5

when you use the right end points,
\[x_k=(k+1)h\]