Fall 2009 Test 1

Fall 2009 Test 1 - + 17 dx 5. (20 points) (a) Compute 2 Z x...

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Math 122 Test 1 September 15, 2009 SI: EF: Name 1 2 3 4 5 Style Points Total Directions: 1. No books, notes or having your two-year old feed the ﬁsh. 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) Compute Z sin x 1 + cos 2 x dx (b) Compute Z x 4 - 1 x dx (Hint: Z u 2 - a 2 u du = u 2 - a 2 - a arcsec ± u a ² + C)
2. (20 points) (a) Compute Z x 3 e x 2 dx (b) Compute Z sin 4 (2 x ) dx

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3. (20 points) (a) Compute Z (tan 21 x )(sec 4 x ) dx (b) Compute Z x x 2 + x - 6 dx
4. (20 points) (a) Compute Z x 3 + x 2 + x - 1 x 2 + 2 x + 2 dx (b) Compute Z x 4 x 2 + 4 x

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Unformatted text preview: + 17 dx 5. (20 points) (a) Compute 2 Z x x 2-1 dx (b) Compute Z 1 x 2 / 3 (1 + x 2 / 3 ) dx FORMULA PAGE sin 2 θ + cos 2 θ = 1 tan 2 θ + 1 = sec 2 θ 1 + cot 2 θ = csc 2 θ sin( α + β ) = sin α cos β + cos α sin β sin( α-β ) = sin α cos β-cos α sin β cos( α + β ) = cos α cos β-sin α sin β cos( α-β ) = cos α cos β + sin α sin β tan( α + β ) = tan α + tan β 1-tan α tan β 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 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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This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.

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Fall 2009 Test 1 - + 17 dx 5. (20 points) (a) Compute 2 Z x...

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