AP Calculus BC : Fundamental Theorem of Calculus with Definite Integrals

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

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Example Question #11 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation

Evaluate the following integral

Possible Answers:

Correct answer:


Evaluate the following integral

Let's begin by recalling our "reverse power rule" AKA, the antiderivative form of our power rule.

In other words, all we need to do for each term is increase the exponent by 1 and then divide by that number.

Let's clean it up a little to get:

Now, to evaluate our integral, we need to plug in 5 and 0 for x and find the difference between the values. In other words, if our integrated function is F(x), we need to find F(5)-F(0).

Let's start with F(5)

Next, let's look at F(0). If you look at our function carefully, you will notice that F(0) will cancel out all of our terms except for +c. So, we have the following:

Finding the difference cancels out the c's and leaves us with 185.

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