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Unformatted text preview: Worksheet for Section 5.3 Evaluating Deﬁnite Integrals
V63.0121, Calculus I Spring 2010
Evaluate the following deﬁnite integrals.
1 x3 − √ x dx π 2.
0 (sin x + 2 cos x) dx 1 3. A company is considering a new product and would like to understand the costs of production. They calculate an initial costs of $3 million to retool their factory for the new product and marginal costs of x2 − 5x + 10 million dollars per million units produced. How much will it cost to produce 2 million units? 3 million? 4 million? 5 million? If you only could choose one of these production levels, which would it be? 4. A model rocket is ﬁred into the air. Over the ﬁrst four seconds, the rocket’s engines give it a velocity of 5t m/s, where t is the time since liftoﬀ. Over the next ﬁve seconds, the rocket continues to move vertically but is now pulled downwards by gravity, so has velocity 20 − 5t. Finally, a parachute unfurls and the rocket falls at velocity −10 + 5e−(t−9) for all t ≥ 9. How high up is the rocket 12 s after liftoﬀ? What is the total distance the rocket travels? 2 ...
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