(a) As an iterated integral, A = B = C = Suppose R is the triangle with vertices (-1,0), (0, 1), and (1,0). [ (3x + (3x + 6y)² dA= R D = B D 1A = √₁² √² (3x (3x + 6y)² dx dy with limits of integration (b) Evaluate the integral in part (a). Hint: substitution may make the integral easier. Integral =
(a) As an iterated integral, A = B = C = Suppose R is the triangle with vertices (-1,0), (0, 1), and (1,0). [ (3x + (3x + 6y)² dA= R D = B D 1A = √₁² √² (3x (3x + 6y)² dx dy with limits of integration (b) Evaluate the integral in part (a). Hint: substitution may make the integral easier. Integral =
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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![Suppose \( R \) is the triangle with vertices \((-1, 0)\), \( (0, 1) \), and \( (1, 0) \).
(a) As an iterated integral,
\[
\iint_R (3x + 6y)^2 \, dA = \int_A^B \int_C^D (3x + 6y)^2 \, dx \, dy
\]
with limits of integration
- \( A = \text{ } \)
- \( B = \text{ } \)
- \( C = \text{ } \)
- \( D = \text{ } \)
(b) Evaluate the integral in part (a). Hint: substitution may make the integral easier.
Integral = \(\text{ }\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18fe6d10-65c6-4dea-a463-83c487832ab0%2F711c5a08-4691-46b7-8980-9cd28f757a65%2F07nmx4_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \( R \) is the triangle with vertices \((-1, 0)\), \( (0, 1) \), and \( (1, 0) \).
(a) As an iterated integral,
\[
\iint_R (3x + 6y)^2 \, dA = \int_A^B \int_C^D (3x + 6y)^2 \, dx \, dy
\]
with limits of integration
- \( A = \text{ } \)
- \( B = \text{ } \)
- \( C = \text{ } \)
- \( D = \text{ } \)
(b) Evaluate the integral in part (a). Hint: substitution may make the integral easier.
Integral = \(\text{ }\)
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