2.) (3x + x2) sin(2x) dx Use whatever method you want to

Q: 1. f(x) = 2x2 – 3x+4 2. f(x) = e-2x sin 5x %3D

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Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

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Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: fe²x+Inx² sin x² dx = +²√e²x cos x² dx

A:

Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: /2 2 cos x dx 1+ (sin x)² -n/2

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Q: ¥2/3 6. cos'x sin x dx 5.

A:

Q: ( sin(3x) e **) + 32- – 4y = 4x (By u x2 (-1-4) (4)(3:5) dx

A: As per the bartleby guidelines for more than one question only one has to be solved. Please upload…

Q: Number 23

A: we have to find definite intregral of given question

Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

A:

Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

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Q: 2. 1- x2dx cos(x + 1) dx 3.

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Q: 2x cos x? dx 1+ sin² x² 8

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Q: 1. § e sin 4x cos 4x dx 2.5 dx Se-2x dx %3D

A: 1) Given:                ∫esin 4x cos 4x dx Apply u-substitution: u=sin 4x⇒du=4 cos 4x dx…

Q: 2 X 1 t3 COS 4- x² dx 2 -2

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Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

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Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

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Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

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Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: Q.2 Find [(x' +5x² – 2) sin 2.xdx . c Inx

A: According to Bartleby Q&A answering guidelines I can answer only one question

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

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Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: 1. f(x) = 2x² – 3x + 4 2. f(x) = e-2x sin 5x 3. f(x) = x cos7 x 4. f(x) = 5 sin 3x – 17e-2x cos 3x…

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Q: B) Find dx dzy and if x = sin 3z and y = tan23z dx2

A:

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

A:

Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

A:

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: 2 2 sin (2t) dt. 8 - cos (2t)

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Q: 11) у%3D V1- sin 2.x y =

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Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: v² operates on sin(-3x) + cos(3y)

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Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

Q: 3) e4x = sin(3x + 4y)

A: