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AP Calculus AB Question Review 2 - Fundamental Theorem of Calculus

The second installment of question reviews to the AP Calculus AB subject

AP exams have begun, and this post finds us reviewing a second concept covered in AP Calculus AB. The first question review covered convavity and the shape of a graph. In this post, the Fundamental Theorem of Calculus is reviewed in further depth as we cover an equation that has both a derivative and an integral. The question is shown below:

What is

The answer choices are:

The concept of the fundamental theorem of Calculus is the only way you're going to be able to solve for this problem. Evaluating the equation shows that you are going to be taking a "derivative of an integral." According to the fundamental theorem of Calculus, the derivative of an integral gives the base function. In other words, the derivative and integral cancel each other out since they are opposite operations of a mathematical equation. Therefore, the answer is simply the base function inside the integral, which in this case is 3cos(3x)

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