Let 9 be the function f: R³ → R, and let C denote the region f(x, y, z) Sketch the region C. Compute the triple integral = 2 x+y - 625 C = {(x, y, z) = R³ | -(5-z) ≤ x ≤ (5-z), (5-z) ≤ y ≤ (5-z), 0≤z≤ 5}. 5 (x+y), ffff dv.

Let A₁ be the set {(x, y): x² + y² ≤ 1} and let A₂ be the set in R2 bounded by the lines y - 2x = -1, y - 2x = 1, y + 3x = 4, and y + 3x = 8. Compute the following integrals by introducing suitable substitutions: (a) | (+s)dedy Question 5 A1 (1-2² - y²) dxdy (b)(

Evaluate the double integral  SSDxydA where D is the triangular region with the vertices (0,0) (3,0) (0,1). The two S are meant to be integral symbols, sorry don't know where I can find them for the keyboard.

Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of S is given by 01/₂√₁+ 11 6₁ 1 + (f(x, y))² dxdy f(x, y) dxdy 2 √¹ - ² () - (or) af 1² dx ду D 2 °1/₂ √√₁ + ( 2 ) + ( )* dxd's af dy D f f 01/√√1+#+ / dx² дуг D xảy dxdy