Question

1. What is the Right Riemann Sum for f(x)=x−3 over the interval [8,11], with n=3 rectangles of equal width?
2. What is the right Riemann sum of f(x)=x+3 when using 3 rectangles in the range [−3,−1]?
3. What is the left Riemann sum of f(x)=−2x+1 when using 2 rectangles in the range [−2,0]?
4. What is the left Riemann sum of f(x)=−3x+2 when using 4 rectangles of equal width in the interval [2,4]?

Answer 1

since the right side of the intervals are at 9,10,11 just add up (1)* f(9)+f(10)+f(11)

Again use the right sides, of width 2/3 each, to get (2/3)*(f(-7/3)+f(-5/3)+f(-1))

Do the left sums similarly, using the appropriate widths.