(b) Solve the following integrals by using substitution and exponential rule and verify the answers. Soe 6e 3*+4

Q: tan' 7x dx

A:

Q: Solve the following Integral Equation: x(0)= 3 =-t +

A: Given ∂x∂t=-t+∫0txtdt with x0=3 We will solve the differential equation using Laplace transform

Q: S (x² – 12x + 100)(6 – x)dx -

A: We can solve as follows

Q: 00 dx 3.

A:

Q: x-1/2 d) -dz e) 5e5x 2x1/2 x-5/2 dx x-3/2 e5x f)

A:

Q: dx VI + V

A:

Q: Solve the integral( x is an exponent):

A:

Q: /2 " sin'e cas Odo

A:

Q: Solve the following Integral Equation: Ho)-2.

A:

Q: In the following equation/s, find the indefinite integral :- see the equation as attached here

A: solution:- Finding indefinite integral:-  an antiderivative of a function f is a function F whose…

Q: Solve the following integrals with detailed steps: dx а. x²/4+x2

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: S. (3-2xtx²) dx

A:

Q: 5. , (6x2 – 3x + 5)d.

A:

Q: 3 -1) da 1 x2

A: The given definite integral is: I=∫123x2-1dx=∫123x-2-1dx=3∫12x-2dx-∫121dx

Q: raluate the following indefinite integral: 4x³ – 5a² + x – 7) dæ |

A: We have to find

Q: In the given equation , select the basic integration formula you can use to find the indefinite…

A:

Q: Solve the following integrals with detailed steps: dx a. x²V4+x2 dx (4-x²)7 b.

A:

Q: find the indefinite integral of the ff   ∫x √x+1dx

A: Given integral is, ∫ xx+1dx.   It is integrated as follows:   Apply u-substitution, u=x+1 ∫…

Q: 24. Solve the following integral using substitution method: f8x√2x² - 1dx

A: Sol:- ∫ 8x2x2-1dxTake the constant out:  ∫a·fxdx=a·∫fxdx=8·∫ x2x2-1dxIntegral Substitution…

Q: 2 x – 4 dx .2 1

A:

Q: What is the value of the definite integral | (-4x° – 3x + 3x – 1) dx? Enter your answer as an exact…

A:

Q: s dx 3x²+2x+5

A:

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: x' +4x + 3 dx x* + 5.x? + 4

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx 2. 4-x-

A:

Q: Solve the following Integral Equation by Method of Successive Approximation:

A: Given: y(x)=1+λ∫011-3xty(t)dt This is in the form g(x)=f(x)+λ∫K(x,t)g(t)dt In the method of…

Q: (x S+ 3x? - 4 ) dx 12

A:

Q: ne J反Inx dx

A:

Q: -st cosht dt

A: We have to solve the definite integral                                                ∫0∞e-stcoshtdt

Q: evaluate the definite integral.

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution . 1.

A:

Q: 2r dr (1 – r)7

A:

Q: Solve the integral. x +1 -dx 4. 4 + x2

A: Our Aim is to integrate the expression given below:-∫x+1x2+4dx -(i)

Q: Evaluate the indefinite integral. S(4Vx- 6x³)dx , and • Identify what is the u=? and du=? Show the…

A:

Q: dx -2 (5-4x- x²)2

A:

Q: 1. dr

A:

Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: Why do you do e to the power of the integral in order to solve the question? Why not just integrate…

A: The objective is to determine the reason for doing e to the power of the integral in order to solve…

Q: хра (q

A:

Q: Find the definite integral of S: (2x – 1)' dæ 2 112

A:

Q: [p'(8+3p*)®dp

A: Given: I=∫p78+3p48dp  ...1   The Power rule: ∫xndx=xn+1n+1+C

Q: 2. S", sec t dt -T/4

A:

Q: 1. (x² – 4x +4)x

A: Given:       ∫x2-4x+443dx    =∫x-2243dx     =∫x-283dx  substitute u=x-2→dudx=1→dx=du        =∫u83du

Q: -2

A:

Q: dx xVx - 1 х —

A:

Q: find the complete integral for equation  p2-q+y2-x2=0

A: Answer

Q: x'-6x+9 3. S

A:

Q: Solve the following Integral Equation: -t + x(0) = 3 %3D

A:

Q: (b) Solve the following indefinite integrals.

A: i. Given integral ∫sinxcos2xdx

Q: Find the the integrals: 3 - 2s ds

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.