1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: 1. (2x4-x3-2x+3) dx 2. (3-2x)2 dx 3. 3(x-1)(2-3x) dx 4. (5-5x+x5) dx 5. 1/3 ex dx 6. (x2-cos x)…

A: The integration is an anti derivative process. it is reverse of the process of differentiation. Here…

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: The solution of sin'x + 2sinx - 3 = 0 on 0°Sx< 180° is:

A: ⇒sin2x+2sinx-3=0⇒sin2x+3sinx-sinx-3=0⇒sinx(sinx+3)-1(sinx+3)=0⇒(sinx-1)(sinx+3)=0⇒sinx-1=0  OR…

Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: 1. Integrate: e3x cos(x) dx

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: sin²x dx cos x

A: To decompose the given integral we have to use some basic trigonometric formulas.   We know that,…

Q: The integral of the given function | cos(9x) cos(5x)dx is equal

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Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

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Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: 5. Find the integral 1 -dx x -5x +6

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Q: .2 -dædy In (x) ey

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Q: 4) f(x)=- - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 cos(3x) +... 12

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Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

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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: Q-3: Find the general indefinite integrals of: 1. S cos ntcos(sin(at)) dt 2. SVx +2x dx s dx 3-2x2-4…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: cos x 3. f sin³x dx (2 + sin?x) + C 3 4. S* x sin 2x dx 1-9x2 5. S sin-1 3x dx + x sin-1 3x + C 3

A: Q - 3

Q: 10 a) Evaluate x cos(5x) dx by using integration by parts.

A: Given:

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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Q: |x²In x dx %3D 13 x'n x- 19 x² +c -x cos x + sin x + c x'3 Inx - x219+ e

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Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: y" +y' = cos 3x

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Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

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Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: sin(4x) cos (2x) dx = +(st)(9) (e) None sin sin (con (2x) Cos сов (10х) sin (2x) sin (10x) (e)( (Cо…

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Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

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Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: 0<x<T (-1)"-1 f(x) = { 27-x COS nX n<x< 27

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Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: =1+ cos (x) x2 + 12x + 20 -dx 1 + cos² (x) 0. At what value of t does the local max of f(t) occur?

A: Given that f(t)=∫0tx2+12x+201+cos2 xdx To find the local maximum of f(t) at t:

Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

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Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: 3. Find the indefinite integral. S (3e* + +x³ + 3) dx

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Q: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: 7/2 in° x cos' xr dx 4

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Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: 4) Evalvate the integral E 4 1+x² dx

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