Q. 13 Write 鈭獵F(x,y)路dr explicitly ... [FREE SOLUTION]

Chapter 14: Q. 13 (page 1106)

Write ${鈭�}_{C} F (x, y) 路 d r$ explicitly as an integral of t, where $F (x, y) = (x^{2} y, x 鈭� y)$ and $r (t) = (2 t, e^{t})$ for role="math" localid="1650821016448" $a 鈮� t 鈮� b$ .

Short Answer

Expert verified

Hence, ${鈭�}_{C} F (x, y) 路 d r = {鈭�}_{a}^{b} {8 t}^{2} e^{t} + 2 t e^{t} 鈭� e^{2 t} d t$

Step by step solution

Step 1. Given Information

Write ${鈭�}_{C} F (x, y) 路 d r$ explicitly as an integral of t, where role="math" localid="1650821779643" $F (x, y) = (x^{2} y, x 鈭� y)$ and role="math" localid="1650821018698" $r (t) = (2 t, e^{t})$ for $a 鈮� t 鈮� b$ .

Step 2. The curve parameterize by r(t)=(2t,et) at a≤t≤b

Thus $r' (t) = (2 + e^{t})$ . So,

role="math" localid="1650822347376" ${鈭�}_{C} f (x, y) dr = {鈭�}_{a}^{b} f (r (t) 路 r' (t) d t {鈭�}_{C} F (x, y) 路 d r = {鈭�}_{a}^{b} ({(2 t)}^{2} e^{t}, 2 t 鈭� e^{t}) 路 (2, e^{t}) d t {鈭�}_{C} F (x, y) 路 d r = {鈭�}_{a}^{b} ({4 t}^{2} e^{t}, 2 t 鈭� e^{t}) 路 (2, e^{t}) d t {鈭�}_{C} F (x, y) 路 d r = {鈭�}_{a}^{b} {4 t}^{2} e^{t} 路 2 + e^{t} (2 t 鈭� e^{t}) d t {鈭�}_{C} F (x, y) 路 d r = {鈭�}_{a}^{b} {8 t}^{2} e^{t} + 2 t e^{t} 鈭� e^{2 t} d t$

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91影视

Write ${鈭�}_{C} F (x, y) 路 d r$ explicitly as an integral of t, where $F (x, y) = (x^{2} y, x 鈭� y)$ and $r (t) = (2 t, e^{t})$ for role="math" localid="1650821016448" $a 鈮� t 鈮� b$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The curve parameterize by r(t)=(2t,et) at a≤t≤b

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91影视

Write 鈭�CF(x,y)路dr explicitly as an integral of t, where F(x,y)=(x2y,x鈭�y) and r(t)=(2t,et) for role="math" localid="1650821016448" a鈮�t鈮�b.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The curve parameterize by r(t)=(2t,et) at a≤t≤b

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Mechanics Maths

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write ${鈭�}_{C} F (x, y) 路 d r$ explicitly as an integral of t, where $F (x, y) = (x^{2} y, x 鈭� y)$ and $r (t) = (2 t, e^{t})$ for role="math" localid="1650821016448" $a 鈮� t 鈮� b$ .