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Lesson Worksheet: The Fundamental Theorem of Calculus: Functions Defined by Integrals Mathematics • Higher Education
In this worksheet, we will practice applying the fundamental theorem of calculus to find the derivative of a function defined by an integral.
Find the derivative of the function .
Suppose that is a function on the interval and we are able to define by . We find that is NOT differentiable on . What can we conclude?
- A is discontinuous somewhere in the interval .
- B is not differentiable everywhere on .
- CThere is a mistake because whenever we integrate a function, it must be differentiable and .
- D is discontinuous everywhere on .
- E is continuous everywhere on .
The figure shows the graph of the function
Which of the following is the graph of ?
- Bnone of the above