# trapezoidal rule

1. (10 points) Find the exact value for the following integral. Show work. 1 x2 + x + 1 0 ( x + 1)2 ( x + 2) dx 2. (10 points) Consider the following integral. Use a.) the Midpoint rule and b.) the trapezoidal rule with n = 6 to estimate the value. Round your answer to 6 decimal places and show work. Keep in mind that x should be measured in radians. /2 0 cos( x 2 )dx 3. (14 points) Consider the following table of values which represents a function y = f ( x) .. 1.5 a. Use Simpson’s Rule in order to approximate the integral f ( x )dx 0 x f ( x) 0 5.0 .25 5.2 .5 5.3 .75 5.6 1 5.9 1.25 5.5 1.5 5.0 b. Suppose we know that f (4) ( x) 2 Estimate the error in your approximation in part (a). c. What would n have to be in order for the error in using Simpson’s rule to be less than 10−6 ? 4. (10 points) Determine if the following improper integral converges or diverges. If it converges, find its value. 1 2 x2 + x dx

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