mt3 - Sample Midterm II 1. (20 points) Find the following...

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Unformatted text preview: Sample Midterm II 1. (20 points) Find the following indefinite integrals (antiderivatives): (a) Z x p x 2- 1 dx (b) Z x √ x- 1 dx (c) Z x cos( x- 1) dx (d) Z cos( x ) 1 + e sin( x ) dx The following formulas may be helpful: Z 1 √ u 2- a 2 du = ln u + p u 2- a 2 + C Z 1 1 + e u du = u- ln | 1 + e u | + C Z 1 1 + e nu du = u- 1 n ln | 1 + e nu | + C 2. (10 points) What is the area of the region bounded by the graphs of y = x 3 and y = 2 x- x 2 ? 3. (10 points) Complete the square in order to use the formula Z 1 √ u 2- a 2 du = ln u + p u 2- a 2 + C to find the antiderivative of Z ( x 2 + 8 x- 9)- 1 / 2 dx 4. (10 points) What is the volume of the solid of revolution formed by rotating the graph of the function f ( x ) = r x- 1 x 2- 2 x- 3 , ≤ x ≤ 1 around the x-axis. 5. (10 points) Let β be a positive constant. Write the antiderivative Z 1 x 2- β 2 dx in terms of β . 1 2 Sample Midterm II Solutions 1a. Using the substitution u = x 2- 1 we rewrite the integral as Z x p x 2- 1 dx...
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This note was uploaded on 10/08/2010 for the course MATH 16b taught by Professor Chuchel during the Winter '08 term at UC Davis.

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mt3 - Sample Midterm II 1. (20 points) Find the following...

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