Exam 15: Integration

Find the indefinite integral dx.

After weeks of radio promotion,a shoe store finds that for the next 30 days its sales change at a rate given by where t is the number of days after the advertising ends and S is in dollars.Find the total sales for the second week after the promotion ends.

The marginal cost function for a manufacturer's product is = 0.0003 - 0.03q + 4,where c is in dollars.If fixed costs are $5000,determine: (a)the manufacturer's total cost function; (b)the manufacturer's average cost function.

dx =

Evaluate:

Suppose the surface area of a 1.7 meter-tall person changes at the rate of = 0.13775 square meters per kilogram,where x is the weight in kilograms.Find the increase in surface area for a person whose weight increases from 70 kilograms to 75 kilograms by evaluating

Determine:

Determine:

A company has determined that its marginal revenue function (in dollars)is given by where x is the number of units sold.Find the total revenue for selling 4 units by evaluating .

Determine:

Determine: dx

Determine

Evaluate: -

If y" = + and y'(-1)= 0 and y(-1)= - ,find y.

Scientists use the formula S = to determine an animal's surface area S (in square meters)from its weight W (in kilograms),where k is a constant that varies from animal to animal.Suppose the scientist studies a certain animal with k = 0.1.Use differentials to approximate the surface area if the animal weighs 124 kilograms.(Hint: Use W = 125.)

A manufacturer of a product has a marginal revenue function given by =200 + 70q - 3 )The demand function for the product is given by

Find the indefinite integral dx.

Determine: dx

Determine: dx

Determine: