Methods of Integration (College Board AP® Calculus AB)

Find the value of .

Show that , where and are integers to be found.

Solve the indefinite integral .

Let the function be defined by .

Let be a function whose derivative is given by on the interval .

Given that , find .

Find the value of . Give the answer in the form , where and are constants to be found.

Water is pumped into a swimming pool at a constant rate of 10 gallons per minute. Water leaks out of the pool at the rate of gallons per minute, for minutes. At the time , the swimming pool contains 15 gallons of water.

How many gallons of water leak out of the swimming pool from time to minutes?

How many gallons of water are in the swimming pool at time minutes?

Write an expression for , the total number of gallons of water in the swimming pool at time . Write the function in the form , where , and are constants to be found and is a function of .

Let be a function defined by

Find the exact value of .

Solve the indefinite integral .

Let be the piecewise-linear function defined on whose graph is given above. Let .

Find .

Solve the indefinite integral .