# Worksheet: The Fundamental Theorem of Calculus: Functions Defined by Integrals

In this worksheet, we will practice applying the fundamental theorem of calculus to find the derivative of a function defined by an integral.

**Q5: **

Find the derivative of the function .

- A
- B
- C
- D
- E

**Q6: **

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 .

**Q7: **

The figure shows the graph of the function

Which of the following is the graph of ?

- A
- Bnone of the above
- C
- D
- E

**Q8: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q11: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q12: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q13: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q14: **

Find the derivative of the function .

- A
- B
- C
- D
- E

**Q15: **

Find the derivative of the function .

- A
- B
- C
- D
- E

**Q16: **

Given that , find .

- A
- B
- C
- D
- E

**Q17: **

Let . Use the Fundamental Theorem of Calculus to find .

- A
- B
- C
- D
- E

**Q18: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q19: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q20: **

Given that , find .

- A
- B
- C16
- D

**Q21: **

Use the Fundamental Theorem of Calculus to find the derivative of the function .

- A
- B
- C
- D
- E

**Q24: **

The graph of a function is shown. Which is the graph of an antiderivative of ?

- A
- B
- C

**Q25: **

The figure shows the graph of the function

Which of the following is the graph of ?

- A(c)
- B(a)
- C(b)
- D(d)