Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x²) – x²)dy = 0

Q: Question 5 Evaluate the multiple integral | cos(x - y) dx dy

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Q: Question 3 What is the general solution of 6y(2y sec2r + tan2r)dx = cos2r(4y- 3sec2x 18y tan2x)dy ?…

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Q: Ap- cos 0 +1 2. Solve the initial value problem. f'(x)= e²* – sin 4.r; f(0)=2 -

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Q: Example 2.34. Apply Muller's method to find the root of the equation cos x = xe which lies between 0…

A: Here we need to use muller's methode.

Q: QUESTION 1 Given y = A cos 3x + B sin 3x ,with constants A and B. (a) Determine the first and second…

A: Given: y=Acos3x+Bsin3xx, with constant A and B. To Find: a. Determine the first and second…

Q: 10 - cln(2n) e cos (e") dx 0. a) О sin (1) b) O e2m - 1 c) O 1 d) O e27 e) sin (1)

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Q: Question 16 Find dy/dx at the given point without eliminating the parameter. X=0 + cos® and y=1+…

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Q: Question 4. (1) [x³² √x² + 4 dx. X3 sin (In x) X (ii) S -dx. Evaluate the integral: (iii) Choose a…

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Q: Question 10 Using the method of Variation of Parameters, the particular solution Y, for the NHLDE…

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Q: Question 11 Consider [x cos²x dx − x sin³x dx = = x+ƒ(x) + — 8(x) + - +C. What is the value of f 8

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Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

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Q: Problem 5. Prove that -dx 1+x (0 <a < 1). sin an

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Q: Question 4 When x°cos (x²)dx is evaluated using IBP, the value of J v du is? A B -cos (x2) cos (x2)…

A: We need to choose correct option.

Q: For equations in the form y = asin(bx + c) + d or y = a cos(bx + c) + d, Its amplitude is equal to:…

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Q: Question 15 Find /dx² at the given point without eliminating the parameter. =0+cos and Y=1+sine…

A: Given: x=θ+cosθ , y=1+sinθ To evaluate: d2ydx2  at θ=π6 We know that we can write dydx=dydθdxdθ

Q: Question 17 Evaluate D3(sinx – 4e) (A) -sin x-32е2х B sin x-32ex -cos x-32 e2x D cos x-32 e?x

A: Solution

Q: Question 5 Solve the following initial value problems. (Hint: Use a similar idea as in Question…

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Q: 1. i) Find ſcos 2x +3 sin 3x dx . ii) Evaluate fxe dx. Hence, solve | 5xe e dx. 1

A: To evaluate the given integrals.

Q: QUESTION 11 The first approximation(p) of the root of the equation f(x) = /x- cos(x) = 0 by Newton…

A: Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation…

Q: Question 1. Find the general solution of the following ODE: y" – 4y' + 3y = -6e² + 40 sin z.

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Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: QUESTION 6 Find an antiderivative of the given function. 3 cos 7x 3 sin 7x sin 7x 7. -21 sin 7x

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Q: Question 2 Find the solution to the Bernoulli Equation. (3siny - 5x) dx + 2x²cotydy=0

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Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: Question 16 Evaluate: [Vx + sin/ dx. A None of the given choices 2x+ cos/x B + C 2 © x+2cosx + C D…

A: As we know that; The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And ∫a·fxdx=a·∫fxdx, where a is the constant.…

Q: QUESTION 10 2x2 – 1 Performing the integration dr yields: (х- 2)3 a. sin -1(x– 3) + c O b. 31n(x- 2)…

A: Follow step below.

Q: Problem 1 Evaluate the indefinite integral.  ∫sin^5(x)cos^4(x)dx= ___________________ +C

A: Given integral can be written as Now, we use following substitution

Q: Question 7 Calculate the integral: /x' cos (2.x²) dx 1 o- sin(2x³) + r cos(2r*) + C b) O sin(2r*)…

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Q: 1.4 = 0.9062 x Cos (1-√³x) dx = 0-6034 How?

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Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

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Q: Problem 8 Evaluate the following Indefinite integral cos 3x dx V5 +2 sin 3x

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Q: QUESTION 9 The solution of the IVP: = 2x+ dx? %3D y(0) = 2 v'(0) = 4 is y(x)= * +2 x sin-x + V1-x²…

A: Initial value problem is an ordinary differential equation having initial conditions on a specific…

Q: Question 20 Solve (x + Vy² – x²) y' – y= 0 O '(÷) - In y - sin O None of the choices O In y – sin )…

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Q: Question 5 Solve the following initial value problems. dy (a) = 6 – 2 cos(3x) and y(0) = 10. d.x dy…

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Q: Question 9 The integral S x dx x²+√√x²-1-1 A /co B / Ⓒece s cose de 1 - sine sec²0 de 1+ tane secᎾ…

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Q: cos (1/x) dx ∞ o COS 21. 12

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Q: Question 22 The solution for the initial value problem -sinx, y()=1 dy is 3D1 dx O a. y=-cosx+1 1…

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Q: 2π π14 cosφ SSS p' sinødp døde 0 0 0

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Q: Question 6 Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions…

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Q: Question 6 a. Solve the following integrals: i. Scos x) sin (-) dx il. SeVI+e*dx

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Q: QUESTION 11 Scos(x) dx Find 1 sin(x) – sin (x) + ar 3 1 cos(x) + cos (x)+ C O 1 sin (x)- 3sin2(x) +…

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Q: QUESTION 2 If y-sin-¹ z, show that d'y Hence, deduce that -(1)-(2) - <- 0. dz = M dz dz

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Q: Question 1 d dx Jx & S" cos(t) dt = O a) cos (x2) · 2x b) cos (x²) · 2 O c) sin (x²) d) sin (t² ) e)…

A: topic - integration and derivatives

Q: Question 1. Determine the following integrals: | 1.1. / 2r sin(a² + 1) dx 1.2. ze

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Q: 95х 3 5X dx b° sin CoS 6

A: The given integral is ∫03π5sin95x6cos35x6dx

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.)…

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: QUESTION 3 a) Evaluate |x2 In | x+1| dx by using integration by parts. b) Use the trigonometric…

A: We apply integration by parts and evaluate the given integration. For part (a) follow 2nd and 3rd…

Q: Question 13 The integral csc(0.5) dx is equal to A None of the given choices B2ln|csc(0.5x) +…

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Q: Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x?) – x?)dy = 0

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