A non-exact equation can be converted to an exact equation by OA. Multiplying with the Integration Factor

Q: 9. f √x³-1dx x

A: Given: I=∫x3-1xdx    ...1 As we know that; ∫11+x2dx=tan-1x+C

Q: In(x) dx Vx

A:

Q: (x- 2x +3)e-° dx.

A:

Q: Give 5 examples of integration by parts with solution

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Q: cln 2 re dr. Use integration by parts to evaluate

A:

Q: What integration technique can be used to integrate: 5√3+x² dx X

A: Follow the procedure given below.

Q: When is the integration method used?

A:

Q: To apply the integration factor method, does the differential equation have to be linear?

A:

Q: 2/3 dx dx V2/3 x³V9x² – 1

A: Integration is defined as mixing things or people together that were formerly separated.

Q: Find the general solution for y''=2t+3 by direct integration and by the method of undetermied…

A: Given that      y" = 2t + 3 Here we have to find the general solution by direct integration and by…

Q: To apply integration factor method, we need to have coefficients?

A:

Q: How do you perform integration by parts?

A: Integration by parts is,

Q: 1 – cos(2x) im —0 1 — сos(6x) - 7* – 6* – 1 im →1 x2 1

A:

Q: 8z + 129z -) dr = (Use Term by term integration)

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Q: -0.3x (49 — х?)о4

A:

Q: 3. у' %3D 2ху — х

A:

Q: Find the Integration of 1 dx. (6x+7)6

A: To find: The integral of ∫dx6x+76. Formula used: Integration formula: Power rule of integration:…

Q: When do we use the method of substitution in integration? Provide an example.

A: Given- Substitution in integration. To explain- The method Substitution in integration. Concept…

Q: dx 8. √√√√x+√√x

A:

Q: 2 x+ 2x dx x°+3x2 – 1

A:

Q: S(x + e*)²dx

A: Solution of question is written in below steps. Note: (a + b)2 = a2 + b2 + 2ab

Q: Find the general solution using Integrating Factors Found by Inspection

A:

Q: What is the formula for integration by parts? Where does it come from? Why might you want to use it?

A: To explain integration by parts with derivation and use.

Q: Give 5 example of Reciprocal rule of Basic Integration Formula.

A: Given: Give examples of the reciprocal rule of the basic integration formula The reciprocal rule for…

Q: (2x+9 9 Jex dx

A:

Q: Integrate by parts: 7x In(x²) dx 2

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Q: Sx In x dx

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Q: | (о + 1) In (») da

A:

Q: Can

A: We use Cauchy's Residue Theorem

Q: Solve the attached equations  by the method of undeterminedcoefficients.

A: Given- d2ydx2-3dydx=e3x-12x To find- The general equation of the above differential equations.

Q: 3 (x²+2)

A:

Q: 12. [ xv2 − xdx x√2

A: ∫x2-xdx

Q: x² ¹ +4x²+1 x6 +2x4+x² -dx

A:

Q: what is the simplification of this integration? ∫dx/(2sinx+3cosx-5)

A: Use sin(x) = 2 tan(x/2) / (1 + tan2(x/2)) cos(x) = (1 - tan2(x/2)) / (1 + tan2(x/2))

Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: xdx √2x-1 1.5.

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Q: Evaluate 3x3 – 2x2 + 4x – 8 - x4 + 4x2

A: Let the given integral be I - I = ∫3x3-2x2+4x-8x4+4x2dx = ∫f(x) dxThen,f(x) = 3x3-2x2+4x-8x4+4x2f(x)…

Q: What is meant by integrating factor?

A:

Q: 5. fe²x sin x dx 2x

A: Given ∫e2x sinx dxTo evaluate the integral:

Q: J1/4 Jx2

A:

Q: Illustrate general features of situations to which integration by parts may be applied?

A: To illustrate: The general features of situation to which integration by parts may be applied:…

Q: Solve the integration by parts | (x² – 2)cosh(x) dx .

A:

Q: Solve any ten Questions of your own choice regarding to integration by parts. with explanation?

A: As per our guidelines we solve only one question.

Q: Please answer this correctly. Double Integration

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Q: biz' dt 2

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Q: 1 3. Jo Txt+1 dx

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Q: dx 17.S (4x²-9)3/2

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Q: Evaluate the indefinite integration. ∫?^3√(1+?^2)??

A: The indefinite integral of any function f(x)=p(q(x)) q'(x) can be evaluated using substitution of…

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.