Integration Question 1a
1. Find the Riemann sums for the following functions.
a) from x 1 to x 5 and n 4.
1.Find the Riemann sums for the following functions.
a) from x 1 to x 5 and n 4.
Answer:
a) -8
1.Find the Riemann sums for the following functions.
a) from x 1 to x 5 and n 4.
Solution:
a) Find the Riemann sum of from x 1 to x 5 for n 4.
hence
i
Substituting in the Riemann sum,
a and x
b, where a \textless b, it is called the definite integral of the function f(x) between the limits of a and b and may be expressed as


, as shown above, then;
For constant Where,
, n
the number of rectangles and f(xi) is the value of f(x) at
. Such a sum is called a Riemann sum. If the limit exists, the area under the curve is exactly equal to the limit of the sum as
This is called the Riemann integral of the function f(x) and expressed as;
Note that as
Hence the Riemann integral of the function f(x) may be written as: