Let R be the rectangle enclosed by the lines y = x, y = x-2, y = -x, and y=-x+3. Sketch region R. Use the transformation u = x-y, v=x+y to sketch region S, the image of region R on the uv-plane. Then use the transformation to make the appropriate change of variables to evaluate the integral f(x+y)e²dA. You must show all the work that leads to your final answer. Give the exact answer in R simplest form. R 0 -5 S 0

Q: The graph attached shows the curves y = x^2 and y^2=x. a.) Discuss the similarities and differences…

A: Here we have to give the differences and similarities between the two graphs that is y=x2  and x=y2.

Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Find the area of the region bounded by the graphs of the equations. y = 5x2 + 3, x = 0, x = 2, y = 0

A: We have to find the area.