اضل وتكامل )2( نظري - طولكرم %3D Question 16 dz sin 1(z) +c dx 6, Not yet answered Select one: Marked out of O True 1.00 O False P Flag question

Q: evaluate the integrals

A: since you have posted multiple questions , so I'll solve first one for you, for rest question's…

Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: 4. sin 'xcos 2 O J sin xcos"xdx (8)

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

Q: 4 2 ["S² sinπTy ³ dydx

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Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: 2 sin(z) + V3 = o %3D

A: Given :   2sin(x) +√3 = 0               2sin(x) = -√3                  sin(x) = -√3/2…

Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

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Q: Ou = 20 · x, du = 5 · sin(5· x) dx %3D Ou = 20 · x dx, du = cos(5 · x) Ou = 5 · x, dv = 20 · cos(x)…

A: we use the rule of integration of uv dx.see 2nd and 3rd step.

Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: 8 Find L-- 8s2+6 sin Vt cos Vt COS V V등 sin y응t COS

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Q: 5. Evaluate 0.1 sinx dx. 1. S, sin(x²) dx 2. S

A: Given the given integrals are (1) ∫01sinx2dx (2) ∫01sinxxdx Use Maclaurin series…

Q: 2 Z = 31 + (Sin 28 + ((ase Ÿ -(Sin@) Fined Iz1 12

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Q: sin y = 1/2 is equal to y = sin (1/2). %3D Select one: O True O False

A: given that sin(y)=(1/2) then y =arcsin(1/2)

Q: 1 sin(2x): -1 sin(2x) 125 %3D (D²-1) True False

A: 1(D2-1)3sin(2x)=1(-22-1)3sin(2x)                             =1(-5)3sin(2x)…

Q: sin 2t sin 5t 10 58s2+ 441 20 s4+58s2 +441 84 O Option 3 Optlon 4 O Option 2 O Nons of the cholcss…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: 3) = + sin (4) r = y(In y- In r+1)

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Q: S(2) = vāsin(5z) sin z

A: Differentiate w. r.t to x

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: =/4 sin z 23)/" dr cosr

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: 5s Evaluate J|2 sin s Jdtds 0 0 I[ 2 OA. 3 (1 – sin(125)) O B. 3 (1+ sin(125)) (1+ cos(125)) 3 OC. 2…

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: sin dx 32 cosS 35 4 Ssin +2 +c cos () • 32 cos + C 32 -cos 32 cos + C 7 4 32 cos 35 즐)-Scos()+기+C

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Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: dø +3ø = sin ot on (0,+∞) dt [$(0) = 1.

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Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 1. Evaluate 2dt a. V5-4t-2t² b. Sdr r2+r-2 3r*+3r³-5r²+r-1 ) sin ()du с. os

A: Explanation of the solution is given below..

Q: Quèstion 3 8+11x dx = 8-11x %3D 1 1 1 O A. 2 + C ++11x 8-11x 11x OB. tan-1 8 64 121x + C |- 1 11x 8…

A: Multiply by sqrt(8+11x) in denominator and numerator.

Q: show that1) d/dz [cosz] = -sin z

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Q: 6. ans. -2cos(1/2)x + C 2 Scos3xdx 7. ans. (1/3)sin3x + C . Stan2vdk 8. ans. (1/2)In(sinx?) + C

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

Q: sin z f(2) = cosz Bring your answer to the simplest possible form.

A: Find derivative 4f as per student required

Q: Əz and Əx az #4. Calculate given that ду x² sin (z) + (x² – 1) y* = 2°.

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

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Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: +z/3 + sin z dz

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Q: f5cos(1-5x) dr = O - 5sin (1 – 5x) + C O -sin (1 – 5x)+ C 一 sin (1 5x) + C 5 - O sin (1 – 5x) + C…

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.