In this worksheet, we will practice solving the line integral of a 2-variable function along a parameterized curve in the plane.

**Q1: **

Evaluate , where , , and for .

- A26
- B13
- C
- D
- E9

**Q2: **

Evaluate , where and .

- A0
- B
- C
- D
- E

**Q3: **

Evaluate , where and .

- A82
- B21
- C
- D
- E9

**Q4: **

Evaluate , where and .

- A26
- B13
- C
- D
- E9

**Q5: **

Evaluate , where is the polygonal path from to to .

- A2
- B5
- C
- D
- E10

**Q6: **

Calculate for the function and curve , where and is the polygonal path from to to .

**Q7: **

Calculate for the function and curve , where and is the path from counterclockwise along the circle to the point and then back to along the -axis.

- A
- B
- C
- D
- E

**Q8: **

Calculate for the function and curve , where , , and .

- A
- B
- C
- D
- E2

**Q9: **

Suppose that is the gradient of the function , and we are given points , and . Choose a starting and an end point from this set so as to maximize the integral , where is the line between your chosen points.

- Afrom to
- Bfrom to
- Cfrom to
- Dfrom to
- Efrom to

**Q10: **

In the figure, the curve from to consists of two quarter-unit circles, one with centre (1, 0) and the other with centre (3, 0). Calculate the line integral , where .

- A
- B
- C
- D
- E

**Q11: **

Calculate for the function and curve , where , , , and .

- A1
- B
- C
- D
- E