Problem :
Consider the function
f (x) = x
^{2} + 1
on the interval
[0, 2]
.
Using four subdivisions, find the left-hand approximation,
L
_{4}
, of the
area under the curve of
f
on the interval indicated.
Δx | = = = | ||
L _{4} | = f (0) + f () + f (1) + f () | ||
= 1 + +2 + | |||
= = |
Problem :
For the same function, using four subdivisions, find the right-hand sum,
R
_{4}
.
R _{4} | = f () + f (1) + f () + f (2) | ||
= +2 + + 5 | |||
= = |
Problem :
For the same function, using four subdivisions, find the midpoint sum,
M
_{4}
.
M _{4} | = f () + f () + f () + f () | ||
= + + + | |||
= = |
Problem : Find
f (x _{k})Δx for f (x) = 2x on [0, 2] |
(2)(4) = 4 |
Problem : Find
f (x _{k})Δx for f (x) = on [0, 3] |