= Evaluate the line integral of f(x, y) = √1 + 9xy, where is the portion of the graph of y 0 ≤ x ≤ 5. Sovit 9xy dS = x³ with
= Evaluate the line integral of f(x, y) = √1 + 9xy, where is the portion of the graph of y 0 ≤ x ≤ 5. Sovit 9xy dS = x³ with
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.1.9
![**Evaluate the Line Integral:**
Evaluate the line integral of \( f(x, y) = \sqrt{1 + 9xy} \), where \( C \) is the portion of the graph of \( y = x^3 \) with \( 0 \leq x \leq 5 \).
\[
\int_{C} \sqrt{1 + 9xy} \, dS =
\]
**Description:** This problem involves calculating the line integral of a given function \( f(x, y) \) over a specific path \( C \), which is defined by the graph of \( y = x^3 \) between \( x = 0 \) and \( x = 5 \). The expression inside the integral represents a function of both \( x \) and \( y \), and the task is to compute this integral along the specified curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91ed8060-678c-4d36-a5c7-0e7a65a577a0%2F8974500b-7fd2-4344-ad7b-44dc3af039f0%2Fo4hvnia_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the Line Integral:**
Evaluate the line integral of \( f(x, y) = \sqrt{1 + 9xy} \), where \( C \) is the portion of the graph of \( y = x^3 \) with \( 0 \leq x \leq 5 \).
\[
\int_{C} \sqrt{1 + 9xy} \, dS =
\]
**Description:** This problem involves calculating the line integral of a given function \( f(x, y) \) over a specific path \( C \), which is defined by the graph of \( y = x^3 \) between \( x = 0 \) and \( x = 5 \). The expression inside the integral represents a function of both \( x \) and \( y \), and the task is to compute this integral along the specified curve.
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