4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

Q: Evaluate the iterated integral. 4z (In(x) xe- dy dx dz J3

A: Formulae used∫e-ydy = -e-y + C∫x2dx    = x33 + C ---------------------------------------- I…

Q: Evaluate the iterated integral. 4 (x² - y²) dy dx -4

A:

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

A:

Q: Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-x

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Q: 1 de is not an improper integral x +1

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: Evaluate the iterated integrals: 4 2 S[x* +xy}dydx 0 1

A:

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: B- Evaluate the following double integrals: .2 .4 1) | (x+ 3y x²)dy dx

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

Q: evaluate the iterated integral.

A: ∫03∫-20x2y-2xy dy dx=∫03∫-20yx2-2x dy dx=∫03x2-2x dx∫-20y dy

Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

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Q: Evaluate the following integral.

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Q: Find the integral. J 3 x√9 - (In x)² + C dx

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

A:

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

A:

Q: Evaluate the following integrals. [e² sec ³ (eª) da 1 2 6 tan¹ x dx I 3 4 √9-w² w² dw pln(4/3) et dt…

A: Given data:- ∫x2dxx2-152, x>1

Q: 9) Calculate the following integrals using the change of Variable (substitution) mothod: 96) 3+2 dx…

A:

Q: Evaluate the iterated integral. V1- x8 dy dx

A: We have to find

Q: Calculate the following integrals: (6X-5)dx 3.1 I = S V3x²-5x+6

A:

Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 а) -dx x² –…

A:

Q: 15. Evaluate the following integrals: (b) , Tax+1)3/2 (c) f, (8)05xdx. 30 8 dx (a) J 7x+5)1/3 ' -dx,

A:

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

A: We have to integrate both

Q: Evaluate the integral. | (In(3.x))² dx = +C

A: From the given problem: I=∫ln3x2dx  ....(1) Let, t=3x So, ddxt=ddx3xdtdx=3dx=13dt Nw substitute…

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

A:

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

A:

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: Evaluate the integral. /9-x2 dy dx dz = /9-x2 (x² + y²)!/2 3 J

A: Straightway, without any further delay, please convert to cylindrical coordinates: x = rcost; y =…

Q: 1. Evaluate the integrals below. 5x²-x +3 (a) J x³ + x (b) [√v √√√x – 1 dx dx

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Q: Which one of the following is a PROPER INTEGRAL? OA. .5 2x dx. 3 7x2-3x O B. dx. x In Oc. | x2…

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Q: 4. Determine the following integrals 4.2 - dx - a x

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Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy d.x - x+4

A: Let's find.

Q: Find the integral by Integration By Parts. 2. 0 cos r0 de 3. cos t dt 4. x² sin x dx

A: Integrating By Parts Rule.

Q: Which one of the following double integrals is equivalent to the integral 2x-x2 Vx2 + y2 dy dx? 0.…

A: The integral in Cartesian coordinates is : We first try to look at the region of integration here:…

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

A:

Q: 4) Evaluate the following indefinite integrals. a. S (+ V3 - dx 4 3x2 b. S (2 sec2 x- 5 cscx cot…

A: Integrare

Q: Evaluate the iterated integral. 18 5 (x + y²) dx dy

A:

Q: Compute the following Gaussian integrals. 1. xte-aa2 dx 8. 2. xe-ax dr

A:

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: 3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this…

A: f(x)= cosx  , [ -π3,π3]as per MVT for Integrals for a function f(x) bounded and integrable on [a,b],…

Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

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Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

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Q: Evaluate the integral.

A: Evaluate the integral.              ∫04-x2x2ydy

Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

A: