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: Evaluate L{t cos 4t} s2 +4 b) 52 – 4 s2 + 16 c) s2- 16 s2 - 16 d) s2-4 a) s2 +4 s2 +16 O a O b

A: None of the options are correct

Q: sten Find the Multiplicity and value for x: a) = (3x + 9)° (2x – 11) (4x – 28)“ - X- values are 3, E…

A: To find the multiplicity and the value for X.

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: 7) T (u, ) -(υ, 2 cos u, 4sin u). Consider the parameterization With 0, y ve (1,3]. u € describing…

A: Direction of normal always positive y axis. So y component of the normal is positive.

Q: For cos2(xy) =-, evaluate y' when x = 1. 4

A:

Q: e5 + - s*) dx= 5*+1 +C I + 1 5 A) True B) False

A:

Q: Evaluate Jsinudu, a, cos u+c b. cos u c. -cos u + c

A:

Q: Evaluate Sæ csc ( * d: *(부) b. - in (esc ()- a. csc + cot + C + cot + C 글미 (무) + cot ()| +c In csc…

A: Evaluate ∫x cscπ-x23dx

Q: If x = u?(u? - 1)2 and y = (3u2- 1)2, then what is the value of dy/dx? A none of the given choices 3…

A: I am attaching image so that you understand each and every step.

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: d dz : (sin(-æ)) = (sin æ). %3D Select one: O a. False. O b. True.

A: The mathematical statement is given by ddxsin-x = ddxsinx

Q: スーマ 2) Lur: メ+2 メ-1

A:

Q: 6x -dx Which of the following is equivalent to (5-x) 2 after appropriate algebraic substitution is…

A: Use the method of substitution to solve a given problem.

Q: Evaluate L, sinh 3t (3

A: L13sinh3tUse the constant multiplication property of Laplace Transform:For function ft and constant…

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

A:

Q: 2. tanx カイ Lim (3, 주 so +1 wi7

A: Explanation of the solution is given below...

Q: dx 4+e¬*

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: B. Let ul,e)=rMsin(nt). Find Pur tru tUge Orr

A:

Q: If f(x) = cos (x) + 3x + 2, x e [0, 1], then f-(5) 3= %3D A) cos + 17. B) 5m cos +17 C) 0. D) 2. E)…

A:

Q: 1) m'n* - (m²n°)*

A: Formula: (Pm)n=pm*n Pm * Pn=pm+n

Q: S dx 4+e*

A: follow next step

Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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: If f(x) = cos (-x) + 3x + 2, xE [0,1], then f"(5) = %3D A) cos + 17. B) cos()+17" (Sm C) 0. D) 2. E)…

A: Solution of question as follows

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

A: let ,  G=∫(7y-2y3)e(y4-7y2)dy

Q: g) u = x³ + 3x²y

A:

Q: Suppose that (ax + b) cos x dx = 12. Then the value of a equals: A) 6. B) -6. C) 6n. D) -6T. E) None…

A: Given: - The integral is, ∫0π(ax+b)cosxdx=12 To find: - The value of a.

Q: 6) Let f f(x)dx 16, f(x)dx 10, fdx 5 then f(x)dx = A)-1 C) 31 B)-11

A: