Reference no: EM132463876

Question 1 - Evaluate

∫∫_{D_c} e^{-x^2-y^2} dA

where D_c is the region in the first quadrant of the xy-plane where x² + y² < c².

Question 2 - Evaluate the integral ∫∫_D(3x - 2y)dA over the parallelogram D bounded by the lines y = 3/2 x - 4, y = 3/2 x + 2y, y = -2x + 1, and y = -2x + 3. Use the linear change of variables

(x, y) = T(u, v)

= (u + 2v, -2v + 3v).

Question 3 - Evaluate

∫∫_D y²/x dx dy

where D is the region between the parabolas x = 1 - y² and x = 3(1 - y²). Use the change of variable (x, y) = T (u, v) = (v(1-u²)).