Find the integral. (Use C for the constant of integration.) [(++ 3)cos( 2 + 6t) at (t + 3)cos( t2 6t) dt

Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A: We can solve this using part method

Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Solve the integral equation S" F(x) cos px dx = ' - P.01 4. .Hence prove that o sin?t -dt = %D

A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p>1

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A: Given differential equation, (x-3y+3)dx + (3x+y+9)dy =0

Q: 1. Find the following integrals. i) S 3e-2x dx 2x2-1 dx ii) S: 2x3-3х

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Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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A: The given integral is, ∫dxa-xb-x To solve the given integral, we use the partial fraction,…

Q: b) - Demonstrate the repeated use of integration by parts by proving the reduction formula п-1 S…

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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: Find the integration to de 0. a+bcos² 0

A: Given ∫02πdθa+bcos2θ. The given integrand is even function  We need to evaluate the above integral.…

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Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

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Q: Find each of the following integrals: dx (x2 + 9)2 a. b. esin z cos x dx 0. 15x2 – 14x – 13 - C. dx…

A: As per our guidelines i can only solve 3 subparts As shown below

Q: Q2/ Find the value of the following integrals: 1- |((x+y)dx + (y – x)dy), when cis given by, x = cos…

A: The integrals in the form ∫C(x+y)dx+(y-x)dy involve the integration over a particular curve C. In…

Q: Q4: Solve the following integrals:- dx 4dx (1) f 2+cos x (2) J sec xesin x (3) Sx sec? x dx dx (4) )…

A: Indefinite Integration

Q: Find the value of dx (7x – 2)° If the integral diverges, give "oo" as your answer. -

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Q: Q2/ Find the value of the following integrals: 1- |((x+ y)dx +(y-x)dy), when c is given by, x = cos…

A: We have to evaluate the integral is ∫cx+ydx+y−xdy. where c is given by x=cosθ, y=sinθ and 0≤θ≤2π.…

Q: dx e2a +5

A:

Q: Q2: Find the value of the following integration, using : 1- Two-points Gaussian integration method.…

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Q: Q1) A-Evaluate the following integrals: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x-2.…

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Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: 2. Reverse the order of integration and then evaluate. o S x² sin(xy)dxdy a.

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

A: Given, ∫01cos2x dx

Q: In the integration of (cos y)^2 dy/(1- sin y), what is the first step to solve the integral? *

A: Given,          ∫cosy2dy1-siny

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: Given integral is

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: 1. Evaluate the following using integration by parts. Show all necessary solutions. (b (e) / re* (d)…

A: As per the guidelines we can solve 1 question only.

Q: 1. Evaluate the following integrals. ? cos(r) dt а. Зx2 — 1 dx b.

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Q: Compute the following integrals. 1 t3 (a) dt. Jo V4+ t² (b) e6x cos (3e2) dx. (Hint: you might need…

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Q: 1. S √x dx VX +1

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Q: Find the integral. e4X cos 3x dx + C

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Q: Q4: Solve the following integrals:- dx (1) ſ; 4dx (2) S; (3) ſ x sec² x dx 2+cos x sec xesin x

A: Since you have posted multiple subparts question in this question so i have solved first three parts…

Q: Q1) A-Evaluate the following integrals: 1) S (cos x/ sin? x) dx. 2) S (2x+4)1/3 dx, use x-0 to x=2.…

A: We have to evaluate the given integration.

Q: 1- xy dy = 0. 1+ xy

A: 1+xyx2y.dx+1-xyxy2.dy=0 (Now multiply both sides by (x2y2) ): y1+xy.dx+x1-xy.dy=0 or,…

Q: Q2/Evaluate the integral: 1.57 9-x2 dy dx x, by changing the order of integration.

A: The integration order can be changed by changing the inner integral to outer and outer integral to…

Q: Solve the following integrals: i. S(e** cos(2x)) dx using integration by parts or tabular method.…

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Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: Q4: Find the integration for the following functions: - (answer three only) sin(lnx) dx 3-…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

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Q: dx S. 2x - 1 e

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Q: Q(1) Find the integral of Vx² – 16 dx

A: Use substitution method to find its integration.

Q: Evaluate the given integrals. 3x dx 1. S 2x*-1

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Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

A: Kindly go through the explanation

Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

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

Q: 1. Perform the integration. Show all necessary solutions. 8t² + sin t sint + cos ty dt co t

A: Find your answer below

Q: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: -4 I cosx (0.25x² + 1.90)dx,use n =3

A: Given:        ∫14cosx0.25x2+1.90dx , n=3 The formula for the Trapezoidal rule:…