Methods of Integration (College Board AP® Calculus BC): Exam Questions

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.

Let be the function given by .

In general, the average value of a function on the unbounded interval is defined to be .

Show that the improper integral is divergent, but the average value of on the interval is finite.

Find the value of in the form where is an integer.

Given that and that the graph passes through , find .

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 .

Evaluate the improper integral , or show that the integral diverges.

Find . Show all of the work that leads to your answer.

Find . Show all of the work that leads to your answer.

Find . Show all the work that leads to your answer.