Test 1 Spring 2008

Test 1 Spring 2008 - sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 1...

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Math 122 Test 1 February 5, 2008 SI: EF: Name 1 2 3 4 5 Style Points Total Directions: 1. No books, notes or losing the game. You may use a calculator to do routine arithmetic computations. You may not use your calculator to store notes or formulas. You may not share a calculator with anyone. 2. You should show your work, and explain how you arrived at your an- swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. 3. You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or you will be penalized. 4. You may leave as soon as you are finished, but once you leave the exam, you may not make any changes to your exam.
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1. (15 points) (a) Z x 3 x - 2 dx (b) Use the formula: Z u 2 u 2 ± a 2 du = u 2 u 2 ± a 2 a 2 2 ln | u + u 2 ± a 2 | + C to evaluate Z e 6 x e 4 x - 4 dx
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2. (20 points) (a) Z x sin x cos x dx (b) Z sin x sec 3 x dx
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3. (20 points) (a) Z tan 3 x cos x dx (b) Z 4 ( x - 1) 2 ( x + 1) dx
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4. (20 points) (a) Z 1 x 2 - 4 dx (b) Z x 2 + 4 x + 6 x 2 + 4 x + 5 dx
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5. (20 points) (a) Z 1 e x + 2 + e - x dx (b) Z 1 sin ± 1 x ² x 2 dx
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FORMULA PAGE
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Unformatted text preview: sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 1 + cot 2 = csc 2 sin( + ) = sin cos + cos sin sin( - ) = sin cos -cos sin cos( + ) = cos cos -sin sin cos( - ) = cos cos + sin sin tan( + ) = tan + tan 1-tan tan sin 2 x = 1-cos 2 x 2 cos 2 x = 1 + cos 2 x 2 sin 2 x = 2 sin x cos x (sin x ) = cos x (cos x ) =-sin x (tan x ) = sec 2 x (sec x ) = sec x tan x (csc x ) =-csc x cot x (cot x ) =-csc 2 x ( e x ) = e x (ln x ) = 1 x (arcsin x ) = 1 1-x 2 (arctan x ) = 1 1 + x 2 (arcsec x ) = 1 | x | x 2-1 x n +1 = x n-f ( x n ) f ( x n ) f ( c ) = f ( b )-f ( a ) b-a f ( c ) = 1 b-a b Z a f ( x ) dx Z 1 x 2 + a 2 dx = 1 a arctan x a + C Z 1 a 2-x 2 dx = arcsin x a + C Z sec xdx = ln | sec x + tan x | + C Z sec 3 xdx = 1 2 [sec x tan x + ln | sec x + tan x | ]+ C Z csc xdx = ln | csc x-cot x | + C 1 + 1 = 2...
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Test 1 Spring 2008 - sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 1...

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