Math  /  Calculus

QuestionThe marginal cost of oil production, in dollars per barrel, is represented by C(x)\mathrm{C}^{\prime}(\mathrm{x}), where x is the number of barrels of oil produced. Report the units of 600C(x)dx\int_{600} \mathrm{C}^{\prime}(\mathrm{x}) \mathrm{dx} and interpret what the integral means.
The units of 600640C(x)dx\int_{600}^{640} C^{\prime}(x) d x are \square

Studdy Solution
Interpret the meaning of the integral 600640C(x)dx\int_{600}^{640} C^{\prime}(x) \, dx.
The integral of a marginal cost function over a specific interval gives the total change in cost associated with producing the additional barrels of oil within that interval. Specifically, 600640C(x)dx\int_{600}^{640} C^{\prime}(x) \, dx represents the total increase in cost when production increases from 600 barrels to 640 barrels.
The units of 600640C(x)dx\int_{600}^{640} C^{\prime}(x) \, dx are dollars\boxed{\text{dollars}}.

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