Description

• Write your name, ID#, and Section number clearly in the very front page.
• Write all answers sequentially.
• Start answering a question (not the pat of the question) from the top of a new page.
• Write legibly and in orderly fashion maintaining all mathematical norms and rules. Prepare a single solution file.

1. Consider the following function: f(x) = ex − x, which is continuous on the interval [1,3]. Use this function to answer the following:
(a) [2 marks] Find the actual integral value for this function.
(b) [10 marks] Use Composite Newton-cotes formula to find the numerical integration for 4 segments.
(c) [4 marks] Compute the error in percentage between the results obtained in the previous two parts. How can we decrease the error more?
(d) [4 marks] Use the Simpson rule to find the numerical integration.
2. Consider the following function: f(x) = 6×2− 4x − 9. Now answer the following questions:
(a) [5 marks] Use the Trapezium rule to numerically integrate over the interval [−2,2].
(b) [3 mark] Compute the exact integrated value of the given function.
(c) [2 marks] Calculate the relative error in percentage.
Motto: Mathematics is NOT difficult, but what is difficult is to believe that mathematics is NOT difficult.