The marginal cost of producing the $x$ th baseball bat is given by:
$C^{'} (x) = 25 + \frac{5 x}{{(x^{2} + 1)}^{2}}$

Find the total accumulated cost for producing the first 10 baseball bats. Round to the nearest cent.

Answer

Expert–verified

Hide Steps

Answer

The total accumulated cost for producing the first 10 baseball bats is $226.23$

Steps

Step 1 ：The marginal cost of producing the $x$ th baseball bat is given by: $C^{'} (x) = 25 + \frac{5 x}{(x^{2} + 1)^{2}}$

Step 2 ：To find the total accumulated cost for producing the first 10 baseball bats, we need to integrate the marginal cost function from 1 to 10.

Step 3 ：The integral of the marginal cost function will give us the total cost function.

Step 4 ：Evaluating the total cost function at 10 and subtracting the value at 1 will give us the accumulated cost for the first 10 bats.

Step 5 ：The total accumulated cost for producing the first 10 baseball bats is $226.23$