Evaluate the improper intergal 1 dx using the residue (x² + 100)² theorem.

Q: Compute the given integral. 1 dx = x² 16 +C

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Q: 3. (5 marks) Evaluate the integral I = dx. Hint: If you need to evaluate fe da, don't! Try a…

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Q: Evaluate the integral. dx 3. xª/x² + 27

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Q: (3t2 – csc(vZt) + 1)' dt (3 In(x) + 2)ev3x dx ((k2 – 3sin(k*))(sin(k³)) dk

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Q: - 7/2 ex -dx cos (e*)

A: We have to find the value of ∫0π2excos5exdx. Let I=∫0π2excos5exdx Put ex=tex dx=dtWhen…

Q: 4) l a sin(ex) cos g dx 3 dx 5) (x - 2)° 3

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Q: 3. 'Evaluate the integral. 5 dx х0.2

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Q: a. Prove that the O.D.E: (2y+2x-5)dx+(6y+2x-1)dy=0 is exact and solve it.

A: First we will check if this equation is exact.

Q: 3. 4.x sin(4x + 5) dx

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

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Q: Evaluate the integral. dx 1

A: givenI=∫13x2dxwe know integral formula∫xndx=xn+1n+1+C

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: .2 dx -2

A: To evaluate  ∫-2bx2-xdx where b is a positive number.

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: 3. Evaluate the integral. (a) -2/3 dx

A: Evaluate the integral

Q: Evaluate the integral: 3 9x dx

A: Given,          ∫3-9x2dx

Q: The approximation of - 1 dx by the composite Trapezoidal Rule with n= 2 is x+4 O 0.40833 O 0.40546 O…

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Q: D 3 (x+z) dx 2) sin Con) de 3 3dx 2

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Q: Question 003: Complete the following question involving Substitution Method. Given the integral dx…

A: Given the integral  I = ∫ 5 sin(4x-1) dx By substitution method, Take u = 4x-1 du = 4 dx  dx = du4

Q: Evaluate the following integral. 2 4 5 dx dy dz -220 245 dx dy dz =| (Simplify your answer.) -22 0

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Q: :S- iven : alue of AB 3 8x+1 4x- dx. If we let the substitution" = 4x-5, the final answer takes the…

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Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: QUESTION 2 a) Evaluate the integral | dx (x-5) +5 b) Show that 5+4x - x² = 9-(x-2) by completing the…

A: (a). From the given problem: I=∫5x-52+5dx   ...1 Let, u=x-5So,ddxu=ddxx-5dudx=1-0du=dx

Q: Evaluate the integral J (1-cos 3x) dx (Cos 6x=2C03 34-)

A: To evaluate the integral, ∫0π1-cos23xdx

Q: Question 006: Complete the following question involving Substitution Method. Given the integral S10-…

A: Consider the given integral ∫10·e5x-8dx

Q: Evaluate the integral. 9. dx ½ (x² (x2 – 1)3/2

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Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: This question requires a full written solution. Find the integral 5x2 - 3x +2 dx (r + 1)(r2 +1) I =

A: Integration by partial fraction

Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Solve the ODE using Galerkin method for two equal length elements d²U + 2 = 0, 0< x< 3 dx2 if u(0) =…

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Q: You are told that Lif(x) dx = 9 and /, 8(x ) dx = -2. what is the %3D value of the definite integral…

A: To Determine: what is the value of the definite integral∫-173fx-4gxdx Given: we have ∫-17fxdx=9 and…

Q: Question 001: Complete the following question involving Substitution Method. Given the integral 2x +…

A: Given:∫e2x+7dx

Q: dx 2 28 — 12х — х

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Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: The integral 4 dy dx is equal to: Select one: 12 6. None of them

A: To determine the value of the integral ∫03∫014 dy dx.

Q: To treat the integral       −36(2x + 1)−2 dx as a constant multiple of one of the form       unu'…

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Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx

Q: Question 8 Using Simpson's method 2 √ ²x³ dx for n = 4 is equal to

A: Simpsons rule

Q: sin TZ Let f (z) = Find the residue of f (z) (z – 3)² at z = 3.

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Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: Can i get help step by step with this problem?

A: Given,

Q: I'm having trouble figuring out why the integral of e-3x dx is equal to (-1/3)e-3x. I do not know…

A: Given:    f(x) = e-3x

Q: Find integral by using rectangular method, 37 Sin(x) enlxt2) dx n=7 15

A: Given: ∫537sinx×lnx+2dx Rectangular method of integral: ∫abfxdx=limn→∞Mn Where, Mn=∑i=1nfmi△x…

Q: Compute the given integral. 1 dx = +C x²+36

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Q: 1) Solve the initial value problem. Show All Your Work. dy 2x+ sec? У(0) %— — 5. - dx 2y

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Q: Question 3: Find the integrali(using u-substitution) Ses (8x+1) dx

A: To evaluate: I=∫cos (8x+1) dx

Q: Using a trigonometric substitution, the integral /- (9+x²)3/2 dx becomes:

A: here option B is true because

Q: 5. Calculate the integral f sin"( 1) cos'( t) dt, Your solution will be an expression in terms of m.…

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Q: Q1-Evaluate the integral 2х — 5 dx - х2 — 5х + 1 3

A: Here I am attaching image so that you understand each and every step.