Question

3. The function $g(u, v) = \left(\frac{u+v}{2}, \frac{u-v}{2}\right)$ maps the right-angled triangle W with vertices at $(-0,0)$, $(0,2)$, $(4,0)$ onto the triangle R with vertices at $(0,0)$, $(1, 1)$, $(-2,-2)$ shown below, (you do not have to prove this). You are are given the function $f(x,y) = x + 2y$. Use the composition $f \circ g(u,v)$ to evaluate $\iint_R f(x,y)dA$. (Any other method will earn you no points.) Write down your work.

Name: 3. The function g(u, v) = ((u+v)/(2), (u-v)/(2)) maps the right-angled triangle W with vertices at (-0,0), (0,2), (4,0) onto the triangle R with vertices at (0,0), (1, 1), (-2,-2) shown below, (you do not have to prove this). You are are given the function f(x,y) = x + 2y. Use the composition f ∘ g(u,v) to evaluate f(x,y)dA. (Any other method will earn you no points.) Write down your work.
Uploaded: 2021-12-29T03:15:41-08:00
Duration: 4 min 34 s
Channel: Ashwani Kumar
Description: 3. The function g(u, v) = ((u+v)/(2), (u-v)/(2)) maps the right-angled triangle W with vertices at (-0,0), (0,2), (4,0) onto the triangle R with vertices at (0,0), (1, 1), (-2,-2) shown below, (you do not have to prove this). You are are given the function f(x,y) = x + 2y. Use the composition f ∘ g(u,v) to evaluate f(x,y)dA. (Any other method will earn you no points.) Write down your work.

          3. The function $g(u, v) = \left(\frac{u+v}{2}, \frac{u-v}{2}\right)$ maps the right-angled triangle W with vertices at $(-0,0)$, $(0,2)$, $(4,0)$ onto the triangle R with vertices at $(0,0)$, $(1, 1)$, $(-2,-2)$ shown below, (you do not have to prove this). You are are given the function $f(x,y) = x + 2y$. Use the composition $f \circ g(u,v)$ to evaluate $\iint_R f(x,y)dA$. (Any other method will earn you no points.) Write down your work.

3. The function g(u, v) = ((u+v)/(2), (u-v)/(2)) maps the right-angled triangle W with vertices at (-0,0), (0,2), (4,0) onto the triangle R with vertices at (0,0), (1, 1), (-2,-2) shown below, (you do not have to prove this). You are are given the function f(x,y) = x + 2y. Use the composition f ∘ g(u,v) to evaluate f(x,y)dA. (Any other method will earn you no points.) Write down your work.

Added by Shawn H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ashwani Kumar

12/29/2021

Step 1

This can be done using the given vertices of the two triangles. Show more…

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Will upvote! na+7 3. The function gu= maps the right-angled triangle W with vertices at (0,0), (0.2,4.0) onto the triangle R with vertices at (0,0), (1,1), (-2,-2) shown below, you do not have to prove this. You are given the function f(x,y)=x+2y. Use the composition f o gu to evaluate ∫z,y dA. Any other method will earn you no points. Write down your work. 2.5 2.0 1.5 1.0 0.5 -0.5 0.5 1.0 1.5 2.0 2.5 Right-angled triangle W Triangle R