Riemann sums: left, right and midpoint practice problems
Left, right and midpoint Riemann sums with a handful of rectangles. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Compute the midpoint Riemann sum \( \displaystyle M_{4} \) for \( \displaystyle f(x) = \frac{3}{x} \) on \( \displaystyle [1, 3] \).
Compute the left Riemann sum \( \displaystyle L_{4} \) for \( \displaystyle f(x) = 12 - x^{2} \) on \( \displaystyle [0, 1] \).
Compute the midpoint Riemann sum \( \displaystyle M_{6} \) for \( \displaystyle f(x) = x^{2} + 1 \) on \( \displaystyle [1, 3] \).
Compute the right Riemann sum \( \displaystyle R_{4} \) for \( \displaystyle f(x) = \frac{5}{x} \) on \( \displaystyle [1, 4] \).
Compute the right Riemann sum \( \displaystyle R_{5} \) for \( \displaystyle f(x) = \frac{4}{x} \) on \( \displaystyle [1, 3] \).
Compute the midpoint Riemann sum \( \displaystyle M_{4} \) for \( \displaystyle f(x) = - x^{2} - x + 13 \) on \( \displaystyle [0, 1] \).
Compute the right Riemann sum \( \displaystyle R_{4} \) for \( \displaystyle f(x) = x^{2} + 4 \) on \( \displaystyle [-1, 1] \).
Compute the right Riemann sum \( \displaystyle R_{4} \) for \( \displaystyle f(x) = 12 - x^{2} \) on \( \displaystyle [0, 2] \).
Compute the midpoint Riemann sum \( \displaystyle M_{5} \) for \( \displaystyle f(x) = 12 - x^{2} \) on \( \displaystyle [-1, 1] \).
Compute the midpoint Riemann sum \( \displaystyle M_{4} \) for \( \displaystyle f(x) = \frac{3}{x} \) on \( \displaystyle [1, 2] \).