B. Integration by Parts 1. xcosx dx

Q: Evaluate using integration by parts. .6 In (x)dx 6 In (x)dx =| 1 (Type an exact answer.)

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Q: Evaluate the integration by parts (5х)(сos(3x))dx 0.

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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: Determine the Integrating factor of the DE: y (2³e™y – 3) dæ + x (y+ x*e®v) dy = 0 -3 1

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Q: (x² y3 + 2y)da + (2.x – 20° y²)dy = 0

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Q: 3. Integration by parts a.j 18x ( x+ 4)»

A: Given

Q: Find the integrating factor of : zydz = (x² + 2y²) dy 1 a. µ 2у3

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Q: Sev dx (Hint: Integrate by parts with u-substitution)

A: To evaluate I=∫exdx

Q: Evaluate the iterated integral. ITT*³. /0 10 6ze-x6 dy dx dz

A: Integrate usually but first with respect to y then x then z.

Q: What is the integrating factor of (1 + cos z) y' = sin z (sin z + sin rcoSI y) - CSC I sin z O1 +…

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Q: Question 3 Selve the linear Ruation: dy 3. Integral faualian.

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Q: dæ 2 (x² + 1)²

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Q: 3. Change the order of integration and evaluate S2 Vx cosx dx dy Xニy 193) y>o

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Q: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

Q: evaluate using Integration by Parts.

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Q: Calculate the iterated integral. 2 (6 7e* + 3y dx dy

A: From the given problem: I=∫02∫067ex+3ydxdy So, we can also write as: I=∫02∫067ex·e3ydxdy

Q: Evaluate the iterated integral. (3x + 4y3) dx dy

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Q: 2. y(2x – y + 1)dx – x(3x – 4y + 3)dy = 0

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Q: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x- 2y – 1) dy=0_

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Q: 10. Swap the order of integration for Só Sà f(x,y)dydx.

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Q: 5y + 5 5 dy 2y e - 5

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Q: raluate the double integral : (x + 2y – 2) dy da

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Q: Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0

A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

Q: (1) Sketch the regions of integration. (a) 3m/2 (b) (r,0)r drdo 3m/4

A: The integrations  (a). ∫-π2π2∫04f(r,θ)rdrdθ(b). ∫3π43π2∫34f(r,θ)rdrdθ We have to sketch the regions…

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

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Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, u is set as: Ox

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Q: Supply the missing integrand and limits of integration. dy (3x² – 2xy + y³) dx dy

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Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: find the integrating factor (xy2-y)dx + (x2y-3x)dy = 0

A: find the integrating factor (xy2-y)dx + (x2y-3x)dy = 0

Q: Use the method discussed under "Integrating Factor found by Inspection". (x² + y² + 1)dx + x(x –…

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Q: Calculate the iterated integral.

A: To calculate the iterated integral ∫05∫142xy4+3dydx

Q: 5. Use integration by parts to evaluate dx. (x+1)2 Hint: Choose u = x.

A: Given that ∫xx+12dx∫xx+1-2dxNote : integration by parts∫fxgxdx=fx∫gxdx-∫dfxdx∫gxdxdxfx=x…

Q: evaluate using Integration by Parts.

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Q: +5y )dx+(2x-4y) dy edary of the region lying between

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Q: M3.1 Integration by Parts (IBP) 1. Sx³e*/2dx S* x sin 2x dx 2.

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Q: 1 Integrate by parts: |xcos x dx 3

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Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: Find the integrating factor for ty' + 2y = t5

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Q: evaluate using Integration by Parts.

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Q: | by inspection: (3y° + xy kdx + (x°y² – 2}kty = 0 1. Integrating factors found

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Q: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: 3 9 a) Change the order of integration and evaluate: S [ dr dy 0 0

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Question 4 Draw the region of integration and evaluate the following integral. LL: 12x2y – y² dydx…

A: We have to evaluate ∫-22∫-x2x212x2y-y2dydx Here we have to first integrate w.r.t y from limits y=…

Q: Part 8. Integration by Parts 8.1 ſy'(a²- y')i dy

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Q: 4 16–x² Change the order of integration. Do Not Evaluate. 5tan xy dy dx

A: Answer