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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