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### Course: AP®︎/College Calculus BC>Unit 11

Lesson 4: AP Calculus BC 2008

# AP Calculus BC exams: 2008 1 a

Part 1a of the 2008 BC free response. Created by Sal Khan.

## Want to join the conversation?

• I don't get why 1/pi is a constant term. Tell me why it is a constant term?
(1 vote)
• 1/pi is a constant term because both the numerator and the denominator are constants. Pi is not a variable. It is equal to 3.14... so the value will ALWAYS be the same when you use it as a divisor.

Hope that was clear.
• Wouldn't it be easier just to evaluate the antiderivative of x^3-4x since the sin of pi x is an oscillating function and effectively the area above zero cancels out with the area below zero.
• the answer is the same thing. i would write down the whole integral but evaluate x^3-4x in my calculator and make it positive. remember this is an AP question
(1 vote)
• Maybe I'm mistaken, but did Sal forget to include a pi when he did the derivative of cos(pi*x) at ?

Also, I don't understand why Sal multiplied -1/pi to -pisinpix when he rewrote the antiderivative of sin(pix). at he says he an just carry it over becuase its a constant but how did he just mulitply it randomly?
• He multiplied it intentionally, as a counter operation to multiplying by pi. This way he is able to complete the antiderivative as pi cosine pi x without changing the overall integral expression.
(1 vote)
• how do we know whether they ask for a negative or positive total area? in another video (link below) the total area is negative.

(1 vote)
• The integral returns the signed area due to how it defined. This can lead to negative area.

Area by definition is always non-negative by definition.

So there are two different concepts signed area and area.
• why cannot directly integrate the function y=x^3-4x on the interval [0,2] ?
(1 vote)
• y=x^3-4x is the lower function, y=sin(πx) is the upper function, and we're trying to find the area between both functions from 0 to 2, so we can just subtract the lower function from the upper function and integrate--in either order, but Sal decided to subtract first.
(1 vote)
• Is this a calculator or no calculator question?
(1 vote)
• You don't need a calculator at all. If you watch the video you can see that Sal solved it completely without the use of a calculator.
(1 vote)
• If I were taking the exam and simply ignored the sin because the integral canceled to 0 would it still be graded as correct?
(1 vote)