Fundamental Theorem of Calculus Part 1 – Derivatives of Integrals
In this video, I demonstrate the Fundamental Theorem of Calculus, Part 1, by solving four complete examples involving derivatives of integrals. The key idea is to understand that the theorem relates the derivative of the integral of a function to the function itself.
We aim to have an expression with a variable in the upper limit of integration and any constant that meets the criteria as the lower limit. With this setup, we can apply the Fundamental Theorem of Calculus to find the derivative. Often, we will need to use the chain rule in this procedure, which several examples in this video will highlight. Additionally, I’ll show how sometimes it’s necessary to split the integral into two parts and also how to flip the limits of integration when needed.
These questions would be representative of something that I would put on a quiz or test and I’d personally I wouldn’t make them any trickier than any of these.
What you will learn:
The process of applying the Fundamental Theorem of Calculus, Part 1, to find the derivative of an integral.
The importance of the chain rule in solving these problems.
How to handle cases where the limits of integration need to be adjusted or split for easier calculation.
Examples of integrating functions with more complex variable limits
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