1. Evaluate the following. Use only the rules and techniques of integration presented in the module. For item (c), find the exact value. In ² (In(ax)) 2.x In(ax) -dr, a> 0 a.

Q: Evaluate the integration by parts (5х)(сos(3x))dx 0.

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Q: 1. Evaluate the following integral: la 2x³ 2x5-x-4x³ + 1 (a) analytically, (b) single application of…

A: NOTE: As per the guidelines we are supposed to answer only 3 subparts question. Please upload it…

Q: Evaluate the following integral.

A: Complete the square of 3 + 2x –x2:

Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

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Q: 2тx + 5 J(x2 + m)

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Q: 2) Refer to sections 1,2,3 in the course notes. Compute the integral: S (3e' – 4 )dt

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Q: Q.1) Evaluate the following integral 2dx x (3(ln z)2 + 12 In r- 15)

A: The given integral is: I=∫2 dxx3 (ln x)2+12 ln x-512

Q: Evaluate the following Integral by using suitable method: 2y3 +y y4 + y² + 1' ª |7 +e-4y . -) dy

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Q: State ALL the theorems on integration used in the following computation: 23 | (3r² – 5)dz = 3 dæ =…

A: Integration is a method of bringing disparate parts together to form a whole. The sum-difference…

Q: xdy-ydx is egual to.... In integration combination x²+y2 A. d(x² + y*) B.dArctan (2) C.dArctan…

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Q: In this question, you are asked to investigate the following improper integral: XPs- 10.1 Firstly,…

A: Since you have asked multiple questions, we will solve the first three subparts for you. If you want…

Q: dæ 2 (x² + 1)²

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Q: Evaluate the following using an appropriate technique of integration. 3x +1 xp- (x² + 1)(2x – 1) (c)

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Q: What is the integral of e^(3.4*x) from x=1 to x=6?

A: Solve the definite integration and put the limit.

Q: Evaluate the following integrals 5z (5 – z°)*dx A. 3 -dr 3 В. 6x + 5 c. /"zV9-z'dz С. 1 -dr 5 - edz…

A: Answer and explanation is given below...

Q: Answer "True" or "False" for the following: x² + 3x – 1 Consider the integral / Edx. Then we can use…

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Q: where does the number that you subsitute in the subsitution method come from? In this case where did…

A: Given,

Q: Sx³(x + 1)3(x – 1)³dx.

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Q: evaluate the integral; ∫ [5,1] t/1+t^2 dt

A: We have to find the value of given definite integral. To find that we use integration by…

Q: 2 V4 – x²dx 0.

A: A detailed solution is given below

Q: Find a, b, c such that the following change of order of integration holds: 3 clnx LL f(x, y)dydx =…

A: The given integral is                 ∫13∫0ln xf(x,y) dydx

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: Write down an explicit solution (involving a definite integral) to the following IVP.  a. y'=…

A: See the solution in the given fig. 1 and fig.2

Q: Use either integration by substitution or integration by parts as needed to evaluate x²+1 x'+3x+5 A…

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Q: 5y + 5 5 dy 2y e - 5

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Q: - Evaluate the following integrals (1) [a - 2)Vzdz (ii) 2-t4)4 t3 dt (iii) / ** – 5x* + 6x² – 18 x3…

A: Solve integration

Q: 7. Evaluate the following integrals. 5x* (a) S ++ sec²x)dx 5x2 (b) S xv7x2 + 12 dx (x + 5) (c) S dx…

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Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

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Q: 2. Evaluate. the fallowing.integrals.a.fter.seveoiag.the areler.of.integratiam. dydx Ans..In)/4 C.…

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Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: Question 14 7 da Calculate the integral: 7a - 6) (x + 2) 8. a) ㅇ윽피-6-mlz + 21 + C 7. b) O In r…

A: Given that: ∫7(x-6)(x+2)dx

Q: In evaluating | x(4 – x)3dx , if we use the substitution that u = 4 – x, then what will be the…

A: Indefinite Integration using substitution

Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

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Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

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Q: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: 3. 2 1 What is the value of the integral 7xyz² dxdydz ? 0.

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Q: 1-Evaluate the following integrals 1/4 a) d x 4. b) SyV4-y dy

A: Consider the given information: To evaluate the integrals.

Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

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Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: If 3 7 f(æ)dæ | f(æ)dæ - f(a)dæ, what are the bounds of integration for the first integral? a = and

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Q: Find the integration inner product on C[–4, 2] of the given functions. f(x) = 15x g(x) = 2x³ %3D…

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Q: Given f (x) = x – z² + 1 %3D - defined over the interval [0, 6]. Use integration methods to solve

A: (a) The interval [1.5, 5] is divided into 8 points, so the 8 points are (1.5, f(1.5), (2, f(2)),…

Q: Evaluate the integral: S dx (x+6)(x-4) ← +C

A: Given problem:-

Q: Evaluate the given integral: x³ – 2Vx dx .3

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Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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Q: If 11 16 F(=)dz = | f(2)dz + f(2)dz – f(=)dr, 11 what are the bounds of integration for the first…

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Q: Evaluate the integral 8t (181² – 3)î + 1?+ 1 t k dt 12 + 1 /

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Q: Solve the following boundary value problems using the finite difference method -2xy - 0, y(0) -0,…

A: Given,      y''-2xy=0, y(0)=0, y(1)=1, with h=0.25