# 2practice-2 - UCLA ID NAME(First Last SECTION X Math 31b...

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UCLA ID: NAME (First, Last) : SECTION X Math 31b Spring 2014 Second Midterm -PRACTICE- Problem Points Grade 1 25 2 25 3 25 4 25 Total 100 Write as neatly and clearly as possible. Feel free to write down the name of a lemma or a theorem that you are using, it could get you partial credit in case you make a computational error (but also: don’t make computational errors). Cheat sheets, cell phones, calculators and abaci are not allowed. You do not need to simplify the final expression of your solution, except in the cases where it is explicitly noted. For each question, place your final answer inside a box.
Problem 1. (25 pts) Compute three of the four indefinite integrals below. Z sin( x ) 2 cos( x ) 2 dx Z 1 x 4 - 1 dx
Z 6 x - 1 18 x p 9 - x 2 dx Z 3 x ( x - 2)( x + 6) dx
Problem 2. (25 pts) Compute two of the four definite integrals given below Z 1 - 1 1 - t 2 (1 + t 2 ) 2 dt Z 1 0 2 t (1 + t 2 ) 2 dt
Z log( ) 0 sin( e x ) e x dx Z 0 sin( x/ 2) - cos( x/ 2) 3 cos( x/ 2) dx
Problem 3. (25 pts) Use whatever integration techniques (partial fractions, integration by
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