# Worksheet: Line Integrals

In this worksheet, we will practice finding the line integral of a scalar function over a curve in 2D and 3D.

Q1:

Evaluate , where , , and for .

• A
• B
• C9
• D13
• E26

Q2:

Evaluate , where and .

• A
• B0
• C
• D
• E

Q3:

Evaluate , where and .

• A82
• B
• C21
• D9
• E

Q4:

Evaluate , where and .

• A
• B13
• C
• D9
• E26

Q5:

Evaluate , where is the polygonal path from to to .

• A
• B
• C10
• D2
• E5

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
• D2
• E

Q9:

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

• A
• B
• C
• D
• E1

Q10:

Calculate for the function and the curve , , , .

• A
• B
• C
• D
• E

Q11:

Calculate for the function and the curve , , , .

• A14
• B
• C
• D
• E

Q12:

Use a line integral to find the lateral surface area of the part of the cylinder below the plane and above the -plane.

• A
• B
• C
• D
• E

Q13:

Calculate for the function and the curve , , , .

• A
• B
• C
• D
• E0