Use the appropriate technique of integration to compute the following antiderivative 1. (x° ln x dx

Q: Sx'ln x dx

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Q: Use order of h® Romberg integration to evaluate 1= f, x e2* dx. Compare ɛa and Eg.

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Q: sV2x - x'dx 2x – x'dx

A: We use appropriate substitution to compute the given integration.

Q: Use Romberg integration to compute R33 for the following integral x sin x dx

A: The solution is

Q: By reversing the order of integration, evaluate the following integral. [ f* x cos (y²) dy dx.

A: Given integral ∫03∫x29xcosy2dydx The objective is to evaluate the integral by reversing the order of…

Q: x³V4 + x?dx 4.

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Q: 2. Sx Arctan x dx

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Q: Use the basic integration rules to find or evaluate the integral. e In(2x) 1+ ln 4 [eind X X dx

A: The given integral ∫1eln2xxdx

Q: I = S(1+ sin x)³ cos x dx

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Q: —x2 — 4х + 18 (Зх+ 4) (x? + 9)"*

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Q: a*cosx dx,a is a constant s

A: Given: ∫axcosx dxa is constant

Q: Evaluate the following by changing the order of integration: dx dy. z/3

A: Explanation of the solution is given below....

Q: Evaluate the integral 0. e dx dy by reversing the order of integration. NOTE: Enter the exact…

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Q: Зх + 108 dx х2 + 2х — 48

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Q: -x2-4x+18 dx (3x+4)(x²+9) 4.

A: Topic = Integration

Q: Evaluate the following integrals (from A to E) A. Integration by parts cos dz i) (3t + t?) sin(2t)…

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Q: [₁ 2x - x² dx

A: To integrate.

Q: Reverse the order of integration and then evaluate the integral. 5 5 sin y dy dx 0 x

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Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

Q: Use numerical integration to evaluate the following: dx (b) e-" sin y dy 2 x(x + 2)

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Q: When approximating f(x) dx using Romberg integration, R4,4 gives an approximation of order:

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Q: 1. x° In x dx

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Q: dx 6. (x² – 4)2

A: Given:

Q: Reverse the order of integration and evaluate the following integral. 2ex2 dx dy 1 c1

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Q: -x2-4x+18 -dx (3x+4)(x2+9)

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Q: Reverse the order of integration in order to calculate the following integral: 2 1+x4 0 dx dy.

A: We can evaluate the given integral by using the integral formulas.

Q: Sx Arctan(x) dx

A: To find:              ∫ x tan-1x dx

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

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Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫Cos √x dx

A: Given: I=∫cosxdx for evaluating given integral, we substitute x=t…

Q: Evaluate the integral. (Use C for the constant of integration.) fa.5* + 9*) dk (1.5× + 9*) dx

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Q: A/2 x+! I Į sin x dy dx -1 0 96.

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Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: )Reverse the order of integration and evaluate the integral dy dx y2 +1

A: Explanation of the solution is given below...

Q: Sx 2 V4 + x´dx

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Q: 6. Change the order of integration and evaluate the integral y+1 у? dxdy -1 Vy+1

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Q: 2) Colculate the following integrals lby integration by ports formula. a) S2x log,x dx 3

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Q: Q4. Using appropriate substitution, find the following integrals using the method of integration by…

A: We use the following results ∫u(x)v(x)dx=u(x)∫v(x)-∫(ddxu(x))(∫v(x)dx)dx ddxe1x=e1x×(-1)x2=-1x2e1x

Q: valuate the following integrals: dx (a) x² Vx² – 16 -

A: As per guidelines we have to solve one question

Q: B: Evaluate the following integral by changing the order of integration: LS dy dx

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Q: | V2x – x2 dx

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Q: dx 1 = J Jaz-x2

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Q: Evaluate the following integral by changing the order of integration: S,2 Vx sin x dx dy y2

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Q: Use the trapezoidal rule of integration to determine the value of the following integrals (a) (b) 2…

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Q: 2. Evaluate the following by changing the order of integration: L' L 40² a dx dy. 2y

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Q: x – 2 dx 9. J x² (x – 1)²

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Q: elx) dx dy

A: We have to find the integral by reverse the order…

Q: Reverse the order of integration and then evaluate. a. Sx? sin(xy)dxdy а. 'y

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Q: x³ V 4 + x2 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the following integral by changing the order of integration: S2 Vx sin x dx dy

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Q: Evaluate the integral. (Use C for the constant of integration) (X^7)/(e^3-5x^8) dx

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