1. Find the Riemann sums for the following functions.
a) from x 1 to x 5 and n 4.
b) from x 2 to x 8 and n 12.
c) from x 2 to x 7 and n 10.
d) from x 4 to x 5 and n 4.
e) from x 1 to x 5 and n 8.
f) from x 2 to x 6 and n 4.
g) from x 4 to x 3 and n 4.
2. Find general expressions for the following Riemann sums for any value of n.
a) from 3 to 5 for
b) from 1 to 4 for
c) from 7 to 6 for
d) from -3 to 0 for
e) from -1 to 2 for
f) from -2 to -5 for
3.Find the Riemann integral of the following functions.
a) from x 1 to x 5.
b) from x 2 to x 8.
c) from x 2 to x 7.
d) from x 1 to x 4.
4. Find the Riemann integral for:
a) from x 2 to x 6
b) from x 1 to x 7
c) from x 3 to x 8
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