6. (4 points) Let R be the triangle formed by the points (1,0), (0, 1), (0, 0). Consider the integral 1₂² (x + y)² cos(x

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6 4 Points Let R Be The Triangle Formed By The Points 1 0 0 1 0 0 Consider The Integral 1 X Y Cos X 1 (189.05 KiB) Viewed 15 times

6. (4 points) Let R be the triangle formed by the points (1,0), (0, 1), (0, 0). Consider the integral 1₂² (x + y)² cos(x² - y²) dA. (a) Explain why it makes sense to apply change of variables to the integral. (b) Define a map T−¹(x, y) = (u(x, y), v(x, y)) from the ry- to the uv-plane which simplifies the integrand. Sketch T−¹(R). (c) Find the Jacobian of T-¹. (d) Evaluate the integral with a change of variables.