1. Compute the following integrals. (a) dx. (b) 2° sin(x³) dx.

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: Evaluate the iterated integral. 5 sin(x + 6y) dy dx

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Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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Q: 2e" dx (e® – 1)2 1

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Q: I. Evaluate the following integrals. 1. Sx sin 3x? dx tan y 2. S dy 1-tan²y 3. S sec?(3 – 2t)dt

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Q: 11. Evaluate the following integrals. sinx dx 1- cosx dt fxsec' x dr b) a) c) t2 +81

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Q: Q1: Evaluate the following integrals by substitution dx 1. e cos e*dx dx 3. J 2x- 3

A: Solve by substitutions

Q: Evaluate the fo llowing integrals S Sin () dx

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Q: Q2 (a) Calculate each of the following integrals. sin 3 0 cos'e 1 S sin x(cosx)4 dx

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Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: Evaluate the iterated integral: 2 sin(xy) dy dx п/2 1

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Q: Calculate the following integrals. In both cases the curve C has a counterclockwise direc- tion: 4.2…

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Q: Evaluate the iterated integral.

A: For iterated integrals of the form ∫ab∫cdf(x)g(y)dydx. They can be simplified to ∫abf(x)d∫cdg(x)dx.…

Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx…

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Q: Calculate the following definite integrals. -1/2 1 dx "dx dt (t+2)³

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

Q: Evaluate the following integrals TC 2x a) -e + sin dx V3x 0. 3. cot(-2x) csc?(-2x) dx b) 7.

A: (a) I=∫0π53x-e+sin-2x3dx =∫0π53x dx-e∫0πdx+∫0πsin-2x3 dx  ∵∫(u+v) dx=∫u dx+∫v dx…

Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

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Q: Consider the following two improper integrals: (1) 1 dx г — 5 -1.7 dx (2) (x –

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Q: Which of the following integrals are improper? (Select all that apply.) dx 5х — 1 dx 2х — 1 sin(x)…

A: An improper integral is a definite integral in which the limits approach a constant, or,…

Q: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

Q: 4. Calculate the following integrals by using the integration methods. (4x* + 8x3 + 15x)dx (a) dx…

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Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: Q2 - Evaluate the following integrals i. S cos5x sin*x dx sinhx dx coshºx

A: See the details solution in below

Q: a) Evaluate the following integrals 1) xe3*dx 2) | x2 sin x dx 3) | x sin 2x dx

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Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

Q: Evaluate the following integrals: dx dx iii)S 1+tan x dx ii) Ja sinx+b cos x 2 sinx+8 cos x dx v)S 2…

A: Given: IV)∫sinh2xdx

Q: Q1) Find the following integrals } 1) S sinh2x sinhx+1 dx 1

A: To solve the given integral

Q: Q2: Evaluate of the following integrals: 4. S sin xcos dx 5. Sxe*dx

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: Evaluate the following integrals: a) sin^4 (2x) cos^7 (2x) dx b) t sin^4 (t^2) dt c) tan^3 (x) dx d)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Q3/A) Evaluate the integrals S sin(ln x)dx

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Q: 2. Evaluate the following integrals. (b) § S, sin y² dy dx

A: Solution

Q: Evaluate the iterated integral. x2 sin(y) dy dx

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Q: 1. Compute the following integrals. (a) dx. (b) x³ sin(æ³) dx.

A: We have to integrate both

Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: 1. Set up the following improper integrals by definition. sin(x) xe-x³ dx dx 2? — Зх — 4 а. с. 7 et…

A: Solution b: Given integration is ∫17exx-1dx Here 1 is the only point of infinite discontinuity So we…

Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

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Q: 1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

A: (a) Given: ∫0πt sin 3t dt Apply integration By part : ∫I.II dx=I∫II dx-∫ddxI∫II dxdx Take: I=t and…

Q: of the following is an improper integral? • In3e COsx dx xe | in(x*+1) dx n(x++1)dr -4 x2-x- 2

A: Improper integrals are characterised as

Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: 3. Find the following integrals. dx S- a. +a?

A: Explanation of the solution is given below...

Q: [9 cos (12 – 6t +1) dt 4

A: Solved below

Q: 5. Calculate the following integrals. (a) / (b) / (c) / sin x cos x dx x sin(x? + 5) dx 3 el/x dx x2…

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Q: 9. Which of the following integrals can NOT be computed using the methods we have covered so far? a)…

A: We have to choose the integral which is not compute by simple integration method

Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

A: