To determine
To make:
A table of thevalues of the right Riemann sums Rn for the integral ∫0πsinx dx with n=5, 10, 50 and 100 then concludeto which value it appears to be approaching.
Answer
2
Explanation
1) Concept:
Use acalculator or a computer to make a table of values of right Riemann sums Rn for the integral ∫0πsinx dx with n=5, 10, 50 and 100.
2) Given:
∫0πsinx dx
and n=5, 10, 50 and 100
3) Calculation:
By using the program in the solution to exercise 4.1.9 with
y=sinx, X min=0, X max= π and different values of n=5, 10, 50 and 100 create a table of values.
So, the table of values of Rn is
n |
Rn |
5 |
1.933766 |
10 |
1.983524 |
50 |
1.999342 |
100 |
1.999836 |
Therefore, from the above table, the values of the right Riemann sums Rn are approaching to 2
Conclusion:
The values of Rn are approaching to 2