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Unformatted text preview: Solution. This integral represents the amount of oil leaked from time t = 0 to t = 120. ± 4. In this problem, we will determine Z e 1 log( y ) dy . (1) Compute d dy ( y (log y-1). Solution. By the product and sum rules, we get d dy ( y log y-y ) = y · 1 y + 1 · log y-y = log y. ± (2) Hence determine Z e 1 log( y ) dy . Date : November 23, 2009. 1 Solution. From the previous part, we see that y log y-y is an antiderivative of log y . Hence, the integral is ( e log e-e )-(1 log 1-1) = 1. ± (3) Also, ﬁnd Z 1 e x dx . Solution. Since an antiderivative of e x is e x , we ﬁnd the integral to be e 1-e = e-1. ± (4) Your answers to parts (b) and (c) should add up to e . Can you explain this graphically? Solution. I will leave this to you. ± 2...
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