handout_11_23

# handout_11_23 - In this problem we will determine Z e 1 log...

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EVALUATING DEFINITE INTEGRALS 1. Evaluate the following integrals. (1) Z 2 0 (6 x 2 - 4 x + 5) dx (2) Z 2 π π cos θdθ (3) Z 1 0 4 1 + x 2 dx (4) Z π/ 4 0 ± 1 + cos 2 θ cos 2 θ ² 2. What is wrong with the following equation? Z 3 - 1 1 x 2 dx = - 1 x ³ ³ ³ ³ 3 - 1 = - 4 3 . Date : November 23, 2009. 1

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3. If oil leaks from a tank at a rate of r ( t ) gallons per minute at time t , what does Z 120 0 r ( t ) dt represent? 4.
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Unformatted text preview: In this problem, we will determine Z e 1 log( y ) dy . (1) Compute d dy ( y (log y-1). (2) Hence determine Z e 1 log( y ) dy . (3) Also, ﬁnd Z 1 e x dx . (4) Your answers to parts (b) and (c) should add up to e . Can you explain this graphically? 2...
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## This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

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handout_11_23 - In this problem we will determine Z e 1 log...

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