Qi/ IR 1f y = show that ゴースメー 2 Rex) = sinh (2X) Ril Compute R cx) when %3D %3D 4 Cosh Vx 4/ Find ú when First stage I Evening mechanical Eng. Deport.

Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: dx 3/2 ca

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Q: 8o lve uaing beta gamma funchon m-1 h-1 dx dy from Me beta funchien formula & elalion X vaies o o1-Y…

A: Given integral is  I=∫01∫01-yxm-1yn-1xydxdy            (i) Now,…

Q: a.) [ sec²(t − 1) dt b.) 2 √t c.) [ sin(Int)

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Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

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Q: Jay ti dx dy Compute the integration

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Q: Q8 Integrate by parts: x sin x dx

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Q: Mesin(2x) dx = e$in(2X) + C then the M is equal to Blank 1 If

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Q: siny µ(x,y) = ye* is an integrating factor of dy 3D0 2e sinxldx cOsy+2e COSX Select one: True False

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Q: e*dx cln 1 Calculate Jin 0.5 V1-ezx" (b)

A: We will solve this integral via substitution:

Q: A. Integration by parts o (3t + t*) sin(2t) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Compute dy/dx in terms of x and y. 20. Thermodynamics texts use the relationship az %3D ax az…

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Q: = Lasin(t") dt y%3D

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Q: (x – y²)dx + 2xydy = 0

A: We have to find integrating factor of given differential equation.

Q: Apply integration by parts: S udv = uv - v – S vdu – J sinx + cosX dx e-X + sinx

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Q: 1 dy J yi + 3y² + 1

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Q: find dy/dx

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Q: dy 3 sinh y - 5 cosh y

A: Given, I=∫dy3sinh y-5cosh y

Q: 2. Integrate: Integration by Parts cos?x dx

A: Given : Integral cos2(x) dx

Q: sinx D.a) Find if mx Vt + 5 dt + siny = x-x²cosy

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

Q: 2) dy 3x-y+1 3y-x+5 Apply homogeneity test to differ en tial equertion cnd solve. %3D

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Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Evaluate using Integration by parts. ∫e4x cos(2x)dx

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Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

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Q: 44. sin(V#) dr First make a substitution, then use integration by parts.

A: At first we make a substitute and then calculate the value of integration by 'By Parts' method.

Q: dx 24. Integrate: J Ve-2x-1 А. Sec 1ex + C В. Sec-1e С. -Sec 1e* +с + C D. –Sec-le-* + C dx 25.…

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Q: A. Integration by parts i) (3t +t²) sin(2t) dt

A: since u have asked multiple question in a single request so we will be answering only first question

Q: 10. Find the most general antiderivative; verify your answer by differentiation. 5-4x 2x" b) f(x)…

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Q: I. Integration by pa 1. Su²sin2u du 2. S y²e2ydy

A: The given integral is,1.∫u2sin2u du2.∫y2e2ydy

Q: Solve using determining the integrating factor: cos x dx + (1 + 2/y) sin x dy = 0. %3D

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Q: 1:10 PM Wed Nov 24 Inverse hy perbolio AUTIVITY Oy = sinh (2x+-1) cosh Sza ☺ y= tanhB | -| /2

A: We have to find the derivative

Q: 4e4sin6x dx secбx Evaluate A) -In|sec6x| + C B 4sin6x + C 1 e4sin6x+ D 4In|sec6x| + C

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Q: Evaluate the integral. cost dt sin n² t - 5 sin t + 4 Select one:

A: We will substitute sint=x, then we will do partial fraction.

Q: 26. (4D4 — 24D3 + 35D? + 6D — 9)у 3D 0. е"C, + с2x) + сз cosh }x + c4 sinh }x. ANS. y =

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Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

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Q: siny µ(x,y) = ye is an integrating factor of ( - 2e-Xsinx)dx +( cosy+2e Xcosx. -)dy = 0 Select one:…

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Q: sinh (z) = %3D e -e 2- e?+ez e2+ez 21 eiz +e-iz 2.

A: We need to find the value of the function sinh(z) Four options are given. So the solution to the…

Q: Can you please check my work for question 14? I know it it hard to follow, but I don't know if I got…

A: The given equation is,

Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

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Q: Q1/ Evaluate 1 dx Jo 1+x² using Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: Simpson's rules are techniques of numerical integration. Both 1/3 and 3/8 rules are explained in the…

Q: Q3/ Solue The Following Simul taneous equatron -y + Sin t + Cost %3D dt where x (6) = 1 ,x') =0,…

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Q: ds Find where Vt +s = 2s . %3D dt

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Q: uct Theorem. 10. K y KM=

A: Solution

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.