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Midterm 1

# Midterm 1 - 2 tan x sec x-1 dx 2 Z x x 4 1 3 dx 3 Z 1 √ e...

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1st Midterm, Calculus 2 Sec 6 02/17/2011 The test is made of 3+1 sets of integrals. Exercises from the first set are worth 10 points, from the second set 15 points, from the third set 25 points. The last two exercises are taken from an integration bee and they are definitely hard; do not waste time on them unless you know what you are doing! You can solve as many exercises as you want from each one of the sets. You are allowed to use primitives from the list included with the test only; everything else must be calculated explicitly. Everything you turn in will be graded and contribute to the final score. Set A (10 points each): 1) Z x arctan ( x 2 ) dx A substitution then integrate by parts 2) Z tan 4 x dx A trig. identity and a substitution 3) Z sin 5 x cos 2 x dx A trig. identity 4) Z x ( x + 1)( x + 2)( x + 3) dx Partial fractions 1

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Set B (15 points each): 1) Z t 5 p t 2 + 1 dt 2) Z arcsin 2 x 1 - 4 x 2 dx 3) Z e x 9 - e 2 x dx 4) Z 1 x ( x 1 3 - 1) dx Set C (25 points each): 1)
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Unformatted text preview: 2 tan x + sec x-1 dx 2) Z x ( x 4 + 1) 3 dx 3) Z 1 √ e x-1 dx 4) Z x 2 + e x + e-x dx 5) Z x 3 p 4 x 2-x 4 dx Set NT 1 (40 points each): 92) Z √ 1-x 2 1 + x 2 dx 93) Z 1 x 2 r x-1 x + 1 dx 1 From the University of North Texas Integration Bee 92/93 2 List of primitives: Z x n dx = 1 n + 1 x n +1 + c ; n 6 =-1 (1) Z 1 x dx = ln | x | + c (2) Z e x dx = e x + c (3) Z cos x dx = sin x + c (4) Z sin x dx =-cos x + c (5) Z sec 2 x dx = tan x + c (6) Z csc 2 x dx =-cot x + c (7) Z tan x sec x dx = sec x + c (8) Z cot x csc x dx =-csc x + c (9) Z 1 √ 1-x 2 dx = arcsin x + c 1 =-arccos x + c 2 (10) Z 1 1 + x 2 dx = arctan x + c 1 =-arccot x + c 2 (11) Z cosh x dx = sinh x + c (12) Z sinh x dx = cosh x + c (13) Z sec x dx = ln | sec x + tan x | + c (14) Z csc x dx = ln | csc x-cot x | + c (15) 3...
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