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short2 - 5(10 pts Determine iF each oF the Following is...

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Exam 2, Day 1 M175-001 Fall, 2009 Name: (1 pt.) 1. (10 pts.) Find the antiderivative. Show all work except for Elementary Antiderivatives. integraldisplay cos 3 xdx 2. (10 pts.) Find the antiderivative. Show all work except for Elementary Antiderivatives. integraldisplay x + 1 2 x 2 - 3 x + 1 dx 3. (15 pts.) For each of the expressions below give the appropriate partial fractions decomposi- tion. You do NOT need to solve for the coefficients in the numerators – leave them as letters. You DO need to complete long division where appropriate. (a) 1 ( x + 3)(3 x + 1) 2 = + + (b) 1 ( x 2 + 4)( x 2 + 2 x + 3) = + (c) x 3 x 2 - 1 = + + 1

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4. (10 pts.) The figure at right shows the graph of f (4) for the function f ( x ) = radicalbig 1 + e - 3 x 2 Find n so that Simpson’s Rule with n intervals will ap- proximate integraldisplay 2 - 2 radicalbig 1 + e - 3 x 2 dx to within 10 - 4 . DO NOT COMPUTE the integral.
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Unformatted text preview: 5. (10 pts.) Determine iF each oF the Following is convergent or divergent. Circle your answer. Reasons are not required, but I will give no partial credit For a wrong answer with no reason. (a) i ∞ 2 x-1 √ x 4 + 2 x dx CONVERGENT DIVERGENT (b) i ∞ 2 x 2 ln x + 2 x 5-3 x 2 dx CONVERGENT DIVERGENT (c) i ∞ 5 x 50 2 e x-x 3 dx CONVERGENT DIVERGENT 6. (10 pts.) Apply a trigonometric substitution to i x 2 √ 1-x 2 dx SimpliFy the new integral to a power oF a single trig Function and then STOP. DO NOT COMPUTE the new integral. 7. (15 pts.) Compute the improper integral. Show all work except For Elementary Antideriva-tives. i ∞ 2 x-2 ln x dx 2...
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