Evaluate the integral by making an appropriate change of variables. 5(x + y) e^(x^2 - y^2) dA, R where R is the rectangle enclosed by the lines x - y = 0, x - y = 9, x + y = 0, and x + y = 5
Added by Alex W.
Step 1
Let's define u = x + y and v = x - y. Then, the Jacobian determinant is |du/dx du/dy| = | 1 1| |dv/dx dv/dy| | 1 -1| which equals -2. The limits of integration for u are 0 and 5, and for v are 0 and 9. The integral becomes: ∫ from 0 to 5 ∫ from 0 to 9 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 89 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integral by making an appropriate change of variables ∬ (x + y)e^(x^2 - y^2) dA where R is the rectangle enclosed by the lines x - y = 0, x - y = 10, x + y = 0, and x + y = 10
Sam S.
Evaluate the integral by making an appropriate change of variables. \[ \int \int_R 3(x + y) e^{x^2 - y^2} \, dA \] where R is the rectangle enclosed by the lines \[ x - y = 0, \] \[ x - y = 8, \] \[ x + y = 0, \] and \[ x + y = 5 \]
Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkouxdh4Ofnmgpwkor7Leaonfpu0Ubfpua B.
Use the given transformation to evaluate the integral: ∫∫R e^(x^2 - y^2) dA, where R is the rectangle enclosed by the lines: x - y = 0, x - y = 4, x + y = 0, and x + y = 5; u = x + y, v = x - y.
Vincenzo Z.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD