1. Evaluate the following integrals using appropriate methods and simplify your answers. (a) ² dr

Q: r In x 2

A:

Q: Find the indefinite integral.

A: Take .

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

Q: 1 Use SUBSTITUTION to evaluate the definite integral to three decimal places. xp- 2x +4

A:

Q: Evaluate the following IMPROPER INTEGRALS, It is optional to double check your answers/solution for…

A:

Q: 1. Evaluate dr x² – 4

A: Given,    ∫1x2-4dx=

Q: 6.) | dx 4 – x²

A: Let the given integral is ∫x34-x2dx

Q: 6t dt +1 5.

A:

Q: Evaluate the following integrals with solution

A:

Q: Evaluate the following indefinite integrals S xe3x² dx and S (x + 4)lnx dx.

A:

Q: 2. a) Evalute the following improper integrals dr 3

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the remaining…

Q: [sin(In x)+cos(In x)]¯ dx

A:

Q: 12.) / 5a2 – 14x + 6 dx 23 – 3r2

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Q: 5х — 2 dx x² +1 - 10.)

A:

Q: (In x) dx x+1 c) d)

A: Definite integration

Q: 2. Evaluate the given definite integral, if it exist. V4 + 3x dx

A: To evaluate

Q: Q1 - Find the reduction formula for each of the following integrals

A:

Q: dx (apply the properties on how to solve improper integrals 1 – x²

A: Given query is to find the value of the integral.

Q: Find the value of the following integral at x-1 S(x² – 1)(x + 1)

A:

Q: Evaluate the following integrals.

A: Evaluate: ∫dxx4-1

Q: Evaluate the following integrals.

A: Given that : The integral is ∫68e2x + 2ex + 17 dx .

Q: In x dx 7.) /

A:

Q: 1

A: ∫x23-1x2dx

Q: 5.) / a In a dx

A: Given, ∫x3lnxdx  Using Integration By Parts, ∫u dv=uv-∫v du Here u=ln(x), dv=x3…

Q: Evaluate the following integral between x=-6 and x=5: 4х — 5 dx -

A: This question is based on definite integral.

Q: 1. 2x + 3 X+1

A:

Q: Solve for the integral of the following using substitution and integration by parts. ∫2x3sin(x2)dx

A: This question is related to indefinite integration, We will solve it using given information.

Q: 2+(In x)3 5. S x((In x)2+ln x) dx

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: 3. Find each of the following integrals using any suitable techniques: (d) sec® 4x tan² 4r dx

A:

Q: /2+In x dx

A:

Q: Evaluate the following integrals.

A: Consider the given integral ∫016dx1-9x2

Q: 4. Evaluate the following real-variable integrals using the method of residues: 2 cos (0) Jo…

A: PART A Consider ∫02πcos2θsinθ+2dθ Let us assume : dz=eiθi dθdz=iz dθdziz=dθ

Q: 1. dr

A:

Q: x Inx dx .2 4. dx 4-x2 3.

A:

Q: 2(x*) dx

A:

Q: Evaluate the following integrals. Reasonable work is expected! 1.) 4x²e" dx

A:

Q: fa- 3v' de 10. far -1 a

A: The power rule of integration is,  We use this rule to solve the given integrals.

Q: 5x (2x x + 6)' dx

A:

Q: 4/3 /3) dx -1

A:

Q: 1. Find the following indefinite integrals. 1 (а) xp /3 – x²

A: We can find the integrations as below

Q: 15. [sec xdx

A: Trigonometric Identity: sec2x=1+tan2x

Q: Q1 - Evaluate the following integrals In(x) dx

A:

Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr…

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

Q: 1. Evaluate the following integrals. Do not simplify! (a) S 7x(3x² + 5)'14dx

A: Given that a)∫7x(3x2+5)14dx b)∫x-3x+8dxc)∫x(4x-1)6dxWe need to evaluate the integral

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: (x 2

A:

Q: Calculate the following indefinite integrals. V-2

A: Given,          ∫x-2xdx

Q: 2. dx

A: Given: ∫ x3ex4-3dx

Q: 2. fx²5-x' dx

A: ∫01x25-x3dxapply u substitution;take, u = -x3;du = -3x2-du3=x2then our equation can be written as…

Q: 6х — 9 4.) dx а2 — Зх + 2

A:

Q: 4. S2-*(5 – x)³dx

A: To integrate the given function