(a) / 3x2 + 5x + 8 dx (x2 + 1)(x + 2) (b) / 2V1– x*dx .5 - (e) J, T- dx 1+ e*

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: In(x) 1. Evaluate -dx if possible. If not possible, explain why.

A: As we know that the integration by parts:- ∫udv=uv-∫vdu

Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: dly dx2 - 2 dy dx -3y = COS X

A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: Use integration to find a general solution of the differential equation        dy/dx = 4x2 + 7

A: Given ,     dydx=4x2+7      dy=4x2+7dxThis is variable seperable form .

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: 2х -1 dx Integrate dx by using substitution method. e*-x+1

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

Q: Solve differential equetion. = 8X+_5X dx 4-202

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Q: Use integration to find a general solution of the differential equation                      dy / dx…

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Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

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Q: Find the particular solution that satisfies the differential equation and initial condintion.…

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Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

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Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: USE EXACT DIFFERENTIAL EQUATIONS To SOLUE THE $OLLOWING: In dx-tn(x=2) 'पर्क - डेण बर =0 y dy dx 3D0…

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Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

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Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

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Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

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Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: 5. dx of y = (1+e-*)²/(1-e-*)

A: We need to find the derivative of the given function.

Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: Find dy/dx at the given point 6x2-5y3=2x-5y at (0,1)

A: First differentiate the equation and then substitute the value of x as 0 and y as 1.

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: A differential equation is said to be exact when ∂M/∂x=∂N/∂y where M and N are its corresponding…

A: Consider the following differential equation: 3x2y-lnx+3ydx-2lnx+xy-3dy=0 M=-2lnx+xy-3N=3x2y-lnx+3y

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: Solve the partial differential differential by separation of variables 3 + 7 0. %3D

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Q: 2xy cos(x^2) - 2xy + 1]dx + [sin (x^2) - x^2]dy = 0

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: Without solving explicitly, classify the critical points of the autonomous differential equation dx…

A: See the solution and follow the steps. You will understand easily.

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: Find oy for dx2

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Q: – (x²- 1) dx using P (1 -;*)-^;* / * m in terms of A?

A: Use simple integration formula.

Q: Obtain the general solution to the equation. 3. dx - (у — 2ху)dy

A: Topic - differential Equation

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

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Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: ind the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: The solution of a differential equation with no unknown constants is a particular solution of that…

Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: 1 B3. Evaluate dx, using substitution method.

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions