AP Calculus BC Free Response Problem Quiz

The video tutorial guides students through solving a calculus BC free response question from the 2008 AP exam. It begins with an introduction to the problem, followed by setting up the definite integral to find the area between two functions. The instructor explains the process of calculating the antiderivative and evaluates the integral to arrive at the solution. The tutorial emphasizes understanding the steps involved in solving definite integrals and antiderivatives, providing a comprehensive walkthrough of the problem-solving process.

Where can you find the free response questions for old AP exams?

• In the AP exam study guide

• On the College Board website

• In the local library

• On educational forums

What are the two functions that bound the region in the problem?

• y = cos(pi x) and y = x^2 - 4x

• y = sin(2pi x) and y = x^2 - 4x

• y = sin(pi x) and y = x^3 - 4x

• y = tan(pi x) and y = x^3 + 4x

What is the purpose of setting up a definite integral in this problem?

• To calculate the area of the region

• To find the volume of a solid

• To determine the slope of a tangent line

• To solve a differential equation

What is the range of x-values used for the definite integral in this problem?

• From x = 1 to x = 3

• From x = -1 to x = 1

• From x = -2 to x = 2

• From x = 0 to x = 2

What is the antiderivative of sin(pi x) used in the solution?

• -1/pi cos(pi x)

• 1/pi sin(pi x)

• -cos(pi x)

• pi sin(pi x)

What is the final calculated area of the region?

• 2

• 3

• 5

• 4

What is the derivative of cos(pi x) according to the chain rule?

• -sin(pi x)

• pi cos(pi x)

• -pi sin(pi x)

• pi sin(pi x)

What happens to the terms involving cosine when evaluated at 0 and 2pi?

• They cancel each other out

• They add up to 2

• They result in a negative value

• They remain unchanged

What is the significance of the minus sign in the antiderivative of x^3?

• It indicates a reflection over the x-axis

• It is part of the subtraction in the integral

• It has no significance

• It changes the direction of the graph

What is the next step mentioned in the video series after solving part A?

• Solving part B

• Reviewing the solution

• Starting a new problem

• Ending the series