Problem 13.1. Calculate the follo gration by parts: (1) Sa sin(3r +1) dx. (2) Sa'e(3r+1 dr. (3) ſ In(2x) dx.

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

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Q: Problem 10: 1, -n <x < 0 {cosx f x) 1 cos-X, 0 < x<t

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Q: Problem 7.2. Using translation and scaling invariance only and Prob- lem 8.1 (linear substitution)…

A: 1) ∫01sin(3x+1)dx2) ∫ABcos(3x+1)dx3) ∫AB(3x+1)51dx Note:   Multiple subpart are given, we are…

Q: Question 8 Find dy/dx of y= sin-!x+ cos-!x dy/dx is Blank 1.

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Q: Problem 1 Solve (x + ex sin y) dx - (y + e* cos y) dy = 0

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Q: 1. 2. (D² -3D+2)y=sine-*

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Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: Problem 3 Use integration by parts to evaluate the integral.…

A: First of all, use substitution method to simplify the integrand.

Q: Example 1 Find dy/dx, if sin (²+3x+¹) b. y = cos²(2x-1)

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Q: Problem #1 Find 4x-5x2 +s dx Problem #2 Calculate f'(t) if fle)=3t°csct Problem #3 d4x-x+3 Calculate…

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Q: Problems 1& 2 involve three functions z(y), y(u), and u(x). Find dz/dx from (dz/dy)(dy/du)(du/dx).…

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Q: Problem 16. (a) Calculate the following antiderivatives: //=/ dx = (b) / -55 (c) / 2e" dx = [ -5 sin…

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Q: Problem 6 (1-cos2x)+2cos²x S V2x + 1 x² dx

A: Solved below

Q: In Problems 1 to 4, integrate with respect to the variable. sin 4x' 1. sin22x sin 2r 2. 3 cos²r 2 3.…

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

Q: Problem 1. Use integration by parts to solve the following integrals (a) Sxe"dx (b) Sx cos(5x)dx (c)…

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Q: Question 12 The Integrating Factor for the DE y dx = (ye-2x)dy is None of These 2y -2y

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Q: -2 S(V2r – 1)2 dr | cos(r) | dx COS

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Q: Question 25 dy The general solution of the DE dx cos²y is %3D A y= cos(x) + C

A: Given:- dy/dx= cos2(y)  To find:- General solution of given differential equation

Q: Question 3 Calculate the integral: 2x sin(3 x) dx 2 2 a) Ox cos(3x) + sin(3x) + C 2 b) O-x cos(3x) +…

A: Apply integration by parts

Q: Question 6 evaluate Sa dx A -sin2x +C B -cos2r + C 2cosx + C 2sinx +C

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Q: dy 1. tanxsin2y = sin²x + cos²y - dx

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Q: 33. tan- (z²y) = x + xy°

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

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Q: In Problems I to 4, integrate with respect to the variable. cos 7t cos 3t 1. sin 5t cos 21 sin2x sin…

A: As per the company guidelines We can first three parts . Please understand. Kindly repost the…

Q: Problem 11 Find the integral.  ∫e^(4x) sin(5x)dx=_________________

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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: SITUATION 5. Find du/dx for the following: * (€);y = VT+ 1 +x² 37. u = sin-1

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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

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Q: problem 1 and problem 2

A: To find the function y =y(x) from the given differential equation satisfying the initial condition

Q: Use the reduction formulas from problem #2, to integrate the following: a) | cos* (3x) dx

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Q: Problem [6 - 8] Use Integration by Parts to verify the specified formulas: 6. fx cos-(2x)dx = x…

A: Solution is given below:

Q: のSX 3 +23 +5y +5y = e + 40 Cos loX-190 Sin lox

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Q: Problem 5 Evaluate the definite integral.  ∫sin^2(6x)cos^2(6x)dx=__________________  (upper limit=7,…

A: Evaluate the integral

Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: Problem 11 Evaluate the indefinite integral.  ∫sec^3(x)dx=____________ +C

A: Given integral can be written as Integrating by parts, we get

Q: /2a cose 2 Se sin æd &d pdp 0 0 0

A: I=∫0π4∫02acosφ∫02πρ2sinφdθdρdφ

Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

Q: Problem 1 Apply trapezoidal and Simpson's rules to the integral 1 1-x dx continually halving the…

A: We have f(x) = y = (1-x2)1/2, using this, we can form the table for f(x) with the corresponding…

Q: Problem 19  Assuming B=/ 0, compute ∫((Asqrt((x^2)-(B^2))/x)dx in terms of A and B.…

A: To evaluate:

Q: * PROBLEM 4 a) Use implicit differentiation to find dy/dx of the function ху (x²y + 1)2 b) Evaluate…

A: a) Given function is  We differentiate both sides with respect to x

Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Question 9 z=cos y Using the substitutions the DE (3cos y – 5x) dx – 2x²tan y dy=0 reduces to dz= –…

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

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Q: 7/2 d sin dx dx COS

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

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Q: Question 12 of 12 fe #0. dz and ye-8 sin 4z = 4z %3D dz dx dz dy II

A: The objective is to find the partial derivatives.