Q1 (a) Evaluate the integration of the following functions: (iii) | (3x3 – 2x 2+1)sinh 2x dx by using tabular method. 1 (iv) fx 2 In 2x dxby using by part integration.

Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A: We can solve this using part method

Q: 3. (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

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Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: У (2ху + 1)dx — хӑу %3D 0 ||

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Q: dx x² V4 – x?

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Q: dx = adt + bdz x = Xo + at

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Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

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Q: Solve the two items using Integration by parts. 1. [x' V9- x² dx 2. Te2* sin x dx

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Q: Q5) Find the integration by using (by part method): S e3X sin X dX

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Q: find tu general Solution of: 2x a) y"-y' - 6y + Cosh = e b) y! -Y = Cosh 2x + Sinh x

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Q: 2 3x 2. Evaluate f x'e* using integration by parts.

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Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

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Q: Q1\| Integrate SIX of the following functions: sinh(lnx)dx 1) 3) | sin?(2x).cos(3x) dx 2) ex. sinxdx

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: dy Q1: Solve the DE x3 dx3 +x = x Inx cos(2lnx) by using inverse dx operator method.

A: Given differential equation is .....1 Its solution is given by yx=C.S + P.I ; where C.S is…

Q: Q4: Solve the following integrals:- dx ³-2x² (1) dx (2) √ √2√9-1² (3) fx² sinxdx (cos-14x)² 1-16x²…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: The integration of dx is 4+x²

A: The given integral ∫dx4+x2 can be evaluated as, ∫dx4+x2=∫dxx2+22                =12tan-1x2+C…

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: . Evaluate using integration by parts 8. (5x - 3) sin(12x)dx = TC 6.

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Q: Q1|| Integrate SIX of the following functions: sinh(Inx)dx 1) 3) f 2) | ex.sinxdx sin (2x).cos(3x)…

A: As per bartleby guidelines we only give first three questions answers.

Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

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Q: f (t) sinh 3t + cosh 3t 2t3 -

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Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

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Q: 8x 4х Q5. Use integration by part to evaluate fe* sin (e** )dx

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: dx J x2-4x+5

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

Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: Calculate the integration y+1 dydx

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Q: Q5. (A) Evaluate [- dx +4x+3 (B) Use integration by part to evaluate ſe* sin (e** )dx

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Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: Q.4 Using the method of substitution the integral fxer-3 dx

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Q: 5. f (t) sinh 3t + cosh 3t – 2t³

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Q: 1. Evaluate the integral 2 4-x² 8x cos y y-4 by reversing the order of integration. dy dx

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Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: (B): Find the integration by using substitution method √x√2x-1 dx

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Q: Sxsin(3x)dx 2

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Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2).…