x+1 Evaluate f dx using the substitution u = 3x - 2 %3D V3x-2

Q: dx Evaluate: ] Vx + 2ax dx Evaluate: V4x – x²

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Q: (21 + V3)/3 11 dx Evaluate 50 + x - 14x

A: Explanation of the answer is as follows

Q: J(x-3x)dx = x' 3x +C 2 -3х + С 4 b. 3x-3+C 3x+C 4 4x* -6x +C

A:

Q: dx dw x'V4-8x (25 + w* } 2.5 V16-9x2 dp- dx 2х (6x -x²)"* 3/2 2. dx 3.5 (5– 4x²)"a 3/2

A: integration

Q: Find f(x) dx = -3.5 -3.5 and 2f(x) – 3 dx = -1

A: Given: ∫-61.5fx=2∫-6-3.5fx=3∫-11.5fx=4

Q: -. Evaluate f³ exp(ar)dr where a > 0

A: Evaluate the integral which is given as, Integration of ex is ex and differentiation of xn=nxn-1…

Q: dx i let x-= 4X-X2

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Q: | f(x)dx if Find f(x)dx = -4 and f(x)dx = 3 9. f(x)dx = i

A: We have to use the properties of definite integral

Q: 5 dx. 2. Evaluate J-∞x²+25

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1-y2 Q2: Evaluate i y² (x? + y²)dx dy

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Q: f (x) = x² + 6x if x = 2 and dx = 0.3, determine dy

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Q: > > f(x) = 2x * d F(x)=(√2x+2/2) f' X+ dx f(x) = , (Vzx) = dx 2√2 x لعلم قواعد العاه م حسب الم d |…

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Q: x* +x-4 Evaluate dx is equal to x² +2

A: ∫x4+x-4x2+2 dx

Q: V1+x3 dx [6] S (7) (ax2a (x2a+1)*dx x-2 ах2а (7] S

A: Given: (1)   ∫1+x33x-2dx (2)  ∫ax2ax2a+13xdx

Q: ¡xr-¹e-λx, x>0, r,λ > 0. Given f(x) Γ(r) 1. Find f(x)dx.

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Q: Integrate the function. dx ,x> 6 x2/x2 - 36

A: Given: ∫1x2x2-36dx , x>6

Q: ODE d²y dx² 1 -|> X dy xp ㅅ X² 1

A: We have to identify the type of the given differential equation. For this, we have to rearrange the…

Q: 3) dx Evaluate : J4x (x² - 3)° dx

A: Given that a integration and we solve by using general formula of integration. We know that…

Q: Evaluate the function: 1 dx x²/3 () 1+a!/3

A: Given: ∫1x231+x13dx

Q: x+2 a) f- =dx V2x-x² |xIn(x+1)dx b)

A: Given that  (a) ∫(x+2)/√(2x-x2) dx   (b) ∫x ln(x+1)dx Here we have to calculate the given integral.

Q: 3 - dx x² – x - 2 (1) (ii) fx'e* dx

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Q: esin¬1 x dx V1-x2

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Q: x(3-5х) J - (3x-1)(х-1)* # 2) Evaluate: -dx-

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Q: arks] (a) Find d dx [1+ Hence evaluate 2x dx. (1+x²)²

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Q: 2 + Vx dx. (a) Evaluate 1 dx. x + x(ln x)2 (b) Evaluate

A: Explained below

Q: dx 3- A) Find a²+ B) Find fx? + Vx – 2 dx C) Find f x'e* dx D) Find fe5x+2 dx

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Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: dx 3- A) Find Ja+x2 a2. B) Find f x2 + Vx –2 dx C) Find f x²e-* dx

A: We have to find the integrals of the given functions.   According to our guidelines we can solve…

Q: dx D3. Evaluate (x²+9)(x²+4)

A: Integration

Q: dx 3- A) Find J a²+x² B) Find ſ x² + Vx – 2 dx C) Find ſ x²e-x dx

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Q: f(x) dx - f g(x)dx - f¹ g(x)dx A. -1 B. 7 C. 1 D. -7

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Q: 10x3 + 6x2 + 9x + 2 9. x + 4 Given %3D x4 + x2 x2 x2 + 1 (10x3 + 6x2 + 9x +2 Evaluate dx (Don't…

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Q: dx 2. Algebraic Substitution f (x+2)vx+1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: f(x) dx =1 then the value of If f(3x +1) dx is %3D ! 1

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Q: x3-3 5). S dx V x11

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Q: 5x 2 Evaluate: f fx fdz dy dx 2

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Q: tix)=Dx²-6xs hurizontal tumpant eme fir). f')=D(x2-6xj Find x-value

A: Answer is The value of x is 0,3,6 And in the given question your differentiation is wrong. Because…

Q: f(x) = 以+3 っ-1 Find dx

A: The given function is: f(x)=x+2x2-1 Therefore, df(x)dx=ddxx+2x2-1          =x2-1(1)-x+22xx2-12…

Q: x² dx. Evaluate: /2x3 -1 -1

A: We have to evaluate the integral

Q: 3x+5 Find S dx (Using substitution method). √3x-7

A: This question can be solved using the concept of integration by substitution.

Q: 2x Evaluate dx using suitable technique. (x² +4)(2x-1)

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Q: 24. f(x + ex)² dx is a. +2ex(x + 1) + b. +2e*(x-1) + x3 c. +2e*(x-1) + d. +2ex(x + 1) + x3 3 ²x + C…

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Q: x dx Evaluate: 3 Va²-x²

A: Let,I=∫xdxa2-x23Now,Let,a2-x2=t-2xdx=dtxdx=-12dtTherefore,I=∫1t3-12dtI=-12∫1t3dtI=-12∫t-13dtI=-12t-1…

Q: x-4 Evaluate dx. (x2 +2x+2) (x-3)

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Q: 3x+2 dx Evaluate | V1-x

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Q: f(x)dx if V3 Find 3 | f(x)dx = -2 and f(x)dx = 4 f(x)dx = 3

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Q: f (x² + 1)e-x dx

A: Given problem:-

Q: (x² - x') 6. Reciprocal Substitution -dx 3

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Q: 5 Find f(x)dxif 2 f(x)dx = -5 and f(x)dx = 2 %3D 5 f(x)dx =i

A: Using integration property ,

Q: dy b. If y = V(B1e* – B2 x³ + B3 x + B4 + In(x))5 , then find the dx A1=1 A2=5 B1=4 B2=6 B3=2 B4=1

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.