**Q1: **

Write the integral for the arc length of the spiral between
and . Do **not** evaluate the integral.

- A
- B
- C
- D

**Q2: **

The purpose of this question is to get improved estimates on the length of a spiral curve.

Use the fact that when to find lower and upper bounds for the length of the spiral between and . Give your answer to 4 decimal places.

- A
- B
- C
- D
- E

By comparing to the average of and when , find better bounds for estimating . Give your answer to 4 decimal places.

- A
- B
- C
- D
- E

**Q3: **

Let be the arc length of the polar curve over the interval . Express as a definite integral.

- A
- B
- C
- D
- E

Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

**Q4: **

Find the total arc length of .

- A
- B
- C6
- D
- E3

**Q5: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q6: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

- A
- B
- C0
- D
- E

**Q7: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

- A
- B
- C
- D
- E

**Q8: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q9: **

Find a definite integral that represents the arc length of on the interval .

- A
- B
- C
- D
- E

**Q10: **

Find the arc length of the polar curve given by on the interval .

- A
- B
- C
- D
- E

**Q11: **

Find the arc length of the polar curve over the interval .

**Q12: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q13: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

- A
- B
- C
- D
- E

**Q14: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C6
- D
- E

**Q15: **

Find the arc length of the cardioid .

**Q16: **

- A
- B
- C
- D
- E

**Q17: **

Find the arc length of the polar curve over the interval .

**Q18: **

Let be the arc length of the polar curve over the interval . Express as a definite integral.

- A
- B
- C
- D
- E

Using a calculator, or otherwise, find the value of giving your answer to 3 decimal places.

**Q19: **

Let be the arc length of the polar curve over the interval . Express as a definite integral.

- A
- B
- C
- D
- E

Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

**Q20: **

Let be the arc length of the polar curve over the interval . Express as a definite integral.

- A
- B
- C
- D
- E

Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

**Q21: **

Find a definite integral that represents the arc length of in the interval .

- A
- B
- C
- D
- E

**Q22: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q23: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q24: **

Find a definite integral that represents the arc length of on the interval .

- A
- B
- C
- D
- E

**Q25: **

- A
- B
- C
- D
- E

**Q26: **

Find the arc length of the polar curve given by the equation on the interval .

- A
- B
- C
- D
- E

**Q27: **

Find the arc length of the polar curve , where lies in the interval .

- A
- B
- C
- D
- E

**Q28: **

- A
- B
- C
- D
- E

**Q29: **

Find the length of on the interval .

- A
- B
- C
- D
- E

**Q30: **

Find a definite integral that represents the arc length of on the interval .

- A
- B
- C
- D
- E

**Q31: **

Let be the arc length of the polar curve over the interval . Express as a definite integral.

- A
- B
- C
- D
- E

Using a calculator, or otherwise, find the value of giving your answer to 3 decimal places.