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StudySheetTest3_09

# StudySheetTest3_09 - Study Sheet for Test 3 Honors Calculus...

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Study Sheet for Test 3 Honors Calculus Keesling Test on 12/8/09 1. Determine the following integrals. Be able to use the following methods and combinations of them to determine the integrals: (1) Substitution, (2) Integration by Parts, (3) Trigonometric Integration, (4) Partial Fractions, and (5) Trigonometric Substitution. (a) tan x dx ! (b) sec x dx ! (c) sin 2 x dx ! (d) cos 6 x dx ! (e) 1 ( x 2 + 2 x + 5) 2 ! dx (f) 3 4 ! 2 x 2 " dx (g) 1 ! x 2 " dx (h) cos 5 a b ! ( x ) dx (i) 2 x 3 ( x 2 + 1)( x 2 ! 1) a b " dx (j) x x 2 ! 5 a b " dx (k) tan 3 ( x )sec 2 ( x ) dx a b ! (l) tan 2 ( x ) + tan 4 ( x ) ( ) dx a b ! 2. Determine the following integrals. (a) 1 x 2 ! 1 " dx (b) 1 x 3 ! 1 " dx (c) x + 1 3 x 2 + 2 dx ! (d) 2 x 2 ( x 2 + 1)( x 2 ! 1) dx " (e) 1 1 + x 2 dx ! (f) 1 (1 + x 2 ) 3 ! dx 3. Determine the centroid of the area bounded by the x– axis, f ( x ) = x n , and the vertical line x = 1 . 4. Determine the centroid of the area within a circle in the first quadrant. 5. Use Pappus’ Theorem to determine the volume of a torus. The torus is the area of a circle of radius a rotated about the y –axis. The center of the circle is distance b from the y –axis.

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