Use the trapezoidal rule of Integration to Jefermine the value of the follawing integrals: Q.1. s (2-x²) dx with ch =1 ) s x . Jx with ch =o.l) b - X e Ś x. In x.dx- with くh=o-1) C.

Q: Evaluate the integral by reversing the order of integration. V3n V3 cos(4x2) dx dy

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Q: Evaluate the integral by changing the order of integration in an appropriate way. x sin z dz dy dx z

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Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

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Q: 81x² Vy? + 16 dy dx ,2 3x

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Q: Evaluate the iterated integral by choosing the order of integration. v3 (2 3y arctan dy dx

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Q: dx XV 16x4 – 1

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Q: Evaluate the integrals in Exercises using integration by parts

A: We know that, Integration by Parts is a special method of integration that is often useful when two…

Q: a) By using integration by parts, find the integral Inx dx. b) Hence, find In Vx dx.

A: We have to apply the integration by parts.

Q: 61. dx dy 3y

A: the given double integral is: ∫01∫3y3ex2dxdy as we can notice that in the given double integral…

Q: Evaluate the integral by reversing the order of integration. 1 r1 = | Vū sin y dydar. I = x2

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Q: Evaluate the integral by reversing the order of integration. 6ely dy dx

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Q: Express the triple integral by using cylindrical COordinotes. SSSR (6+x+y) dV where R is bounded…

A: Take projection on to xy plane and use the cylindrical coordinates dV=r dr dt dz

Q: Use the 4-segments multiple Trapezoidal rule to estimate the integral L VI+ z*dz

A: Given that  The integral is  To find the integral by using trapezoidal rule

Q: For the given integral, draw the region of the integration, reverse the order of integration to…

A: We need to reverse the order of integration for the following integral ∫01∫x2xfx,ydydx

Q: Calculate the integral by interchanging the order of integration. 2, (x + 7e – 6) dx ) dy

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Q: Evaluate the integral by reversing the order of integration. dx dy

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Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: B:Reverse the order of integration, then evaluate the following integral: ex dydx + dydx

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Q: S. v cos (x*) dx dy

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Q: Use a CAS double-integral evaluator to find the integrals. Then reverse the order of integration and…

A: Given information: The integral is ∫12∫0x21x+ydydx. Calculation: Evaluate the integral…

Q: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

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Q: By reversing the order of integration, evaluate the double integral 4y Vx2 + 1 dx dy :=y²

A: The region of integration is bounded by the parabola x=y^2 , vertical line x=1, x-axis and y=1  The…

Q: First make a substitution and then use integration by parts to evaluate the integral. ecos t sin 2t…

A: The definite integral to be solved is  ∫0πecostsin2tdt

Q: ydy (y–1)*

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Q: Evaluate the integral. (Use C for the constant of integration.) In(Vx) dx

A: ∫lnxdx=∫lnx12dx=12∫lnxdxLet u=ln(x)du=1xdxdv=dxv=∫dxv=x

Q: 1. Evaluate the integral by reversing the order of integration. re dy dr.

A: we only solve one question at a time. Please send these questions separately which you want to be…

Q: Evaluate the integral using lIntegration by Partsisubstitution, or both if necessary. In(In 10x) dx…

A: Rewrite the given integral as shown below: ∫lnln10x10xdx=110·∫lnln10xxdx

Q: хIn x dx х Arctan (x) dx

A: The given integral is ∫x9 ln x dx Note:     Multiple questions are given, we are answer only one…

Q: Approximate the value of the gven Integral by ase of the Trapezoidal Rule, using the giveu Value of…

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Q: Evaluate the integral using integration by parts. x e 11x. *dx xp, e 11x dx = to

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Q: Evaluate the integral by changing the order of integration in an appropriate 1 1 In7 2× sin (xy³)…

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Q: Evaluate the integral by reversing the order of integration. re* dx dy lo J3y

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Q: Evaluate the integral by using u-substitution and changing the limits of integration. 3x dx J, ex++1

A: ∫-103xex4+1dx Let say, u=x4 Therefore, du=4.x3.dx  ⇒ x.dx=du4x2=du4u. x=-1 ⇒u=1x=0⇒u=0 Therefore,…

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫z(ln z)2 dz

A: Since, we have to evaluate the integral given below:-∫z(ln z)2dz -(i) using substitution and…

Q: Evaluate the integral using tabular integration by parts. (2 x² – x +3) e +C -

A: We can evaluate the given integral by the tabular integration by parts method.

Q: sin(e" – y) dy dx - In x

A: We have to find integral given in question.

Q: Evaluate the integral by reversing the order of integration.

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Q: Evaluate the integral using tabular integration by parts. 8 x³ V2 x + 1 dx +C

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Q: Evaluate the integral using tabular integration by parts. 2 x³ /2 x+1 dx +C

A: Recall the tabular integration by parts

Q: Calculate the integral by interchanging the order of integration. 16, dy ) dx 1

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Q: Consider the integral a* In(x) dx: Applying the integration by parts technique, let и — and dv dx…

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Q: Evaluate the integral by changing the order of integration in an appropriate way. 18 + z) dx dy dz…

A: Evaluation of triple integrals by Using order of change of integrals

Q: Evaluate the integral by reversing the order of integration. So Soy e dædy =

A: Given: ∫01∫8y8ex2dxdy

Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: Use an appropriate change of variable to evaluate the double integral: ソーx COS dA, y+ x R where R is…

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Q: Use an appropriate change of variable to evaluate the double integral: dA, y+x cos R where R is in…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Consider the integral z'e* Applying the integration by parts technique, let and

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.