Math 122 Test 1 Fall 2007

# Math 122 Test 1 Fall 2007 - x(tan x 1 dx(b ∞ Z e-1/x x 2...

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Math 122 Test September 18, 2007 Name 1 2 3 4 5 Style Points Total Directions: 1. No books, notes or orange barrels. 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) Use the formula: Z u 2 u 2 ± a 2 du = u 8 (2 u 2 ± a 2 ) u 2 ± a 2 - a 4 8 ln | u + u 2 ± a 2 | + C to evaluate Z x 8 4 x 6 - 1 dx (b) Z ln x x 2 dx
2. (20 points) (a) Z (cos x ) (csc 2 x ) dx (b) Z (sin 2 x ) (sec x ) dx

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3. (20 points) (a) Z sec 4 2 x tan 2 x dx (b) Z 4 x - 1 x 2 + 2 x - 3 dx
4. (20 points) (a) Z 1 x 2 4 + x 2 dx (b) Z x x 2 + 4 x + 8 dx

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5. (20 points) (a) Z sec 2 x tan
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Unformatted text preview: x (tan x + 1) dx (b) ∞ Z e-1 /x x 2 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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Math 122 Test 1 Fall 2007 - x(tan x 1 dx(b ∞ Z e-1/x x 2...

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