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A university-level mathematics assignment from the intermediate calculus course taught by dr. Khalili at christopher newport university during the spring 2008 semester. The assignment includes two problems: the first problem involves using simpson's rule to approximate the definite integral of cos(x^2) dx with an accuracy of 10^-6, and the second problem deals with finding the value of the constant 'a' that makes the integral of (x^2 + 4 - (2x + 3) / x) dx convergent, and then evaluating the integral for that value of 'a'.
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Christopher Newport University Mathematics Department
Dr. Khalili Math 240 Intermediate Calculus Spring 2008 Maple Project 3 Due at April 4
Problem1. Find
1
cos(x^2 ) dx to within an accuracy of 10−^6 , using Simpson’s Rule.
Hint: Use the error estimate formula for Simpson’s Rule to find the required n.
Problem2. Find the value of the constant a for which the integral
∫ (^) ∞
0
( (^) x x^2 + 4
a 2 x + 3
dx
is convergent. Evaluate the integral for this value of a.
