Refer to the following Venn diagram. 12 A 3 B 15 20 U Find the following. (a) n(A n B) (b) n(A©n BC) (c) n[(A n B)°] (d) n(AC U BC) (e) n[(A n BC) U (Aº n B)] (f) n(U^)

Q: Ixe A) e¯(1 − x) + C el-r 1-x B) -I dx = +C x C) -e (x + 1) + C D) −æe¯ª + C E) e(x + 1) + C

A: Topic = Integration

Q: x, 5 1 + 8 #3) Evaluate:S (e*(4 + e*)° 8-3x + . 1+x

A: Given the integration of ex(4+ex)5+1/(8-3x) + 8/(1+x2).

Q: Q2. Consider the ODE Using u = y ¹, we get A) u' - xu = sin x B) u + 2xu = - 2 sin x C) u + xu = sin…

A: The given differential equation is       y’ - xy = y2sin x    . . . . . . . . . . . . (1)    Now, we…

Q: ce(U) cl (D) {U. H} (J (H) {D. D'] = a (D')

A:

Q: Which of the following is equivalent to 2cos2(θ)−6csc2(θ)+2sin2(θ)+6cot2(θ)? a) −4 b) 8 c) 2tan(θ)…

A: solution:step 1:Givenwhich of the following equivalent to:2 cos2θ-6 cosec2θ+2 sin2θ+6 cot2θnow, 2…

Q: 2 2y³) e³¹-7y²dy. Evaluate (7y - 2y³) (7y -

A: let ,  G=∫(7y-2y3)e(y4-7y2)dy