Exam 15: Integration

The acceleration of an object after t seconds is given by y'' = 32,the velocity at 0 seconds is given by and the position at 2 seconds is given by Find y(t).

dx =

Determine:

Find the indefinite integral dx.

Find the differential in terms of x and dx. y = ln

If = - 4x + 1 and y(3)= 8,find y.

Evaluate: where f(x)=

Evaluate:

The income (in dollars)from a clothing store is increasing at a rate of f(t)= 500 where t is in weeks.Find the total income for the store between the sixth and twelfth weeks.

Determine:

Suppose the rate of savings in a country is given by = 5.1 + 400 + 6000,where t is the time in years,and S is the amount of money saved in billions of dollars.Find the function S(t)which gives the total amount of money saved.You may assume that $0 is saved at t = 0.

Determine:

Determine:

Use differentials to approximate .

Find dy if y = (5 + .

Determine:

If the rate of change of a company's revenue can be modeled by = 3 ,then find r(t)the revenue function.

When an object is moved from one environment to another,its temperature T changes at a rate given by ,where t is the time (in hours)after changing environments,C is the temperature difference (original - new)between the environments,and k is a constant.If the original environment is 40°,the new environment is 100°,and k = -2,then find T(t).

Use differentials only to find an approximate value of .

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 = 0.3.Use differentials to approximate the surface area if the animal weighs 65 kilograms.(Hint: Use W = 64.)