6) Let f(x) = 2x² on [1,6].
(a) Sketch the right Riemann sums with n = 5 then calculate the right Riemann sums. Determine whether this Riemann sum underestimates or overestimate the area under the curve.
(b) Sketch the left Riemann sums with n = 5 then calculate the left Riemann sums. Determine whether this Riemann sum underestimates or overestimate the area under the curve.
(c) Sketch the midpoint Riemann sums with n = 5 then calculate the midpoint Riemann sums.
(d) Use sigma notation to right Riemann sum with n = 50.
(e) Use definite integral to find the area under f(x) on [1,6].
