In: Advanced Math
(a) Find the Riemann sum for
f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2,
with six terms, taking the sample points to be right endpoints.
(Round your answers to six decimal places.)
R6 =
(b) Repeat part (a) with midpoints as the sample points.
M6 =
If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b | f(x) dx |
a |
≤ M(b − a).
Use this property to estimate the value of the integral.
4 | 4
|
||
0 |
(smaller value) |
(larger value) |