Chapter 14: Q. 10 (page 1106)

Write the first alternative form of $\int_{C} G (x, y, z) \cdot d r for G (x, y, z) and C_{2}$ from Example 3. (This alternative form is described immediately after Definition 14.4 and is used in Exercises 5–8.)

Short Answer

Expert verified

The alternative form of $\int_{C} G (x, y, z) \cdot d r is \int_{C} e^{y} dx + x e^{z} dy + y^{2} dz$

Step by step solution

Step 1. Given Information

Write the first alternative form of $\int_{C} G (x, y, z) \cdot d r for G (x, y, z) and C_{2}$ from Example 3. (This alternative form is described immediately after Definition 14.4 and is used in Exercises 5–8.)

Step 3. From the example 3 F(x,y,z)=(ey, xez,y2)

Now writing the alternative form of $\int_{C} G (x, y, z) \cdot d r$

$\int_{C} G (x, y, z) \cdot d r = \int_{C} e^{y} dx + x e^{z} dy + y^{2} dz$

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Write the first alternative form of $\int_{C} G (x, y, z) \cdot d r for G (x, y, z) and C_{2}$ from Example 3. (This alternative form is described immediately after Definition 14.4 and is used in Exercises 5–8.)

Short Answer

Step by step solution

Step 1. Given Information

Step 3. From the example 3 F(x,y,z)=(ey, xez,y2)

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Write the first alternative form of ∫CG(x,y,z)·drforG(x,y,z)andC2 from Example 3. (This alternative form is described immediately after Definition 14.4 and is used in Exercises 5–8.)

Short Answer

Step by step solution

Step 1. Given Information

Step 3. From the example 3 F(x,y,z)=(ey, xez,y2)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write the first alternative form of $\int_{C} G (x, y, z) \cdot d r for G (x, y, z) and C_{2}$ from Example 3. (This alternative form is described immediately after Definition 14.4 and is used in Exercises 5–8.)