Thm. ①) [V₁ +V₂] 8 − [V₁]₂ + [V2]g ⑦ [av] 3 - α [V]₂ 2 3 V=O [v]8 ≤V=0 [V]₂ = 0

Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y – 2y³ + exy+ y) is analytic.

. Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

Find R f(x, y) dA where f(x, y) = 3x + 1 and R = [1, 2] × [−2, 4]. SSR f(x, y) dA = Submit answer Next item

x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y, (b) y/(x+y), (c) |x- yl.

Compute - dx. X +2 Ox-2in|x| + C + C 2+ 2x Ox-2injx + 21 + C (* + 2)2 +C

Evaluate (xy + yz + xz)dV B B = {(x, y, z) | 0 < x < 2,0 < y < 2,0 < z < 4} .

Evaluate p(x² + y²)5/2 dA, where D = {(x, y) E R² | 0 < y < 1, - VI- y² < a < 0}.

EVALUATE Sx csc(2x) cot(2x) dx A. -zse (27) + la (ese (2) – cot (2-) + C B. z csc (2z) +In csc (2z) – cot (2x) +C C. -z cse (2r) - In (ese (2r) – cot (2) +C 1 D. rcsc (2z) -In (cse (2z) – cot (2r) + C

Evaluate J₁ (xy + yz + xz)dV B B = {(x, y, z) | 0 ≤ x ≤ 10,0 ≤ y ≤ 10,0 ≤ z <10}.