Math  /  Calculus

QuestionA company finds that the marginal profit, in dollars per foot, from drilling a well that is xx feet deep is given by P(x)=2x3P^{\prime}(x)=2 \sqrt[3]{x}. Find the profit when a well 200 ft deep is drilled.
Set up the integral for the total profit for a well that is 200 feet deep. P(200)=0()dxP(200)=\int_{0}^{\square}(\square) \mathrm{dx}

Studdy Solution
The profit when a well 200 ft deep is drilled is approximately $5130\$5130.
The integral setup is: P(200)=02002x3dxP(200)=\int_{0}^{200} 2\sqrt[3]{x} \, \mathrm{dx}

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