Try It Yourself#
Exercise 1#
Using a right Riemann sum with 3 subintervals of equal length, approximate
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Answer: \(13/12\)
Exercise 2#
Using a left Riemann sum with 3 subintervals of equal length, approximate
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Answer: \(63\)
Exercise 3#
Evaluate
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Answer: \(e^6/3 + 95/9\)
Exercise 4#
Find the area under the graph of
over the interval \([e^4, e^7].\)
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Answer: \(33/2\)
Exercise 5#
The marginal cost function associated with producing \(x\) widgets is given by
where \(C'(x)\) is measured in dollars/unit and \(x\) denotes the number of widgets. If the daily fixed costs incurred in the production amount to \(\$600\), find the total cost incurred in producing the first 100 units of the day.
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Answer: \(\$6,100\)
Exercise 6#
Evaluate
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Answer: \(\frac{1}{4}\ln(\frac{21}{5})\)
Exercise 7#
Evaluate
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Answer: \(1/32\)
Exercise 8#
Compute the average value of
on the interval \([-2, 2]\).
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Answer: \(-2/3\)