Wyx %3D If w = e* + x In y + y In x prove that Wgy

Q: Evaluate the double integral S S (11a°y³ + 11eš")dædy

A: We have to evaluate ∫36∫2611x3y8+11e5x dxdy   We evaluate this double integral using iterated…

Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: In lns Ing Ss H.w X. 2 dy dx Drad ad Evaluade the Aner expressd by be above ndagral

A: given       ∫0lnln8∫y=exln8exeydydx=

Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

A:

Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: Evaluate the integral 1 2 s s хе dx dy -1

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Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

A: Given

Q: Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we…

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Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…

A:

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

A:

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: Evaluate the double integral: ∬ 4y/(1+x2)dydx y runs from 1/2 to 2 x runs from 0 to 1

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Q: 9 Open on a Jamboard Set beckground Clear frame ha: y=5 %3D 2x+ Vai X =4 %3D Domain hole: none…

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

A:

Q: In(x) Evaluate the iterated integral: dx dy xy 1. 1.

A: For solving this double integral, first we have to integrate w. r. t x , while doing so we have to…

Q: iv) if zy = (x)- then zx + Zy = %3D %3D

A:

Q: 3. Evaluate the iterates integral: SL(x-y) dy dx

A: We have to solve

Q: - Evaluate the integral dx using Simpson's th rule e* – 1 3 -

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Q: Prove that Jn (x) X good dx=1. n

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Q: 2. If A = f+ g,+ hy s.t f(x.y.z) = e2x, g(x.y.z) = xcosy, h(x. y. z) = log 2z then div A %3D %3D

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Q: Tind dʻz of z- In (xy) Find d²z z - In (xy)

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Q: Find the general solution of the DE dyldx = y(x – y) /x^2. O y = C/ In(y) O y = C/ In(x) O y = x /…

A:

Q: IN SA Coefticients 4 Linear in two vanabtes: (x-34+4) dx+2(x-ソ-2)dy

A: In the question it is asked to solve the equation using coefficients linear in two variables:

Q: Integrates PDE SE ニー Zく Z8 te

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Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: dz If z = xy ln(x + ythen ду MC8.2.pdf I y х| In(x + у) + x + y У In(x + у) + x + y O y(1 + In x +…

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Q: (a) Evalate the integral||xydy dx. 12

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Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

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Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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Q: In z 25 If the triple integral So" Sõ So™² (xe¯y) dydx dz Find the upper limit value E.

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Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

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Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: The general solution for D. E. e'y' – + e' = 0 is - x² +xy O y = e¬* + In ( Inlx|+c x+y-1 O y = -x +…

A:

Q: 3 Evaluate the improper integral :S e2 dx

A: e-198

Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

Q: Compute the flux

A: by divergence theorem flux=∫∫sF.ds   =∫∫∫E div F dv Given F=x,y,zand   S; is the boundary of the…

Q: In(x) -dx Evaluate the integral m(2)

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Q: If x = k (1+ e*) dy _ x² + x°ew/ s° +2yeb/a} prove that dx 2xyely/x}

A: NOTE: Refresh your page if you can't see any equations. . ................(1)

Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

A:

Q: Compute the integral 4x /5 – e2¤ dx. e

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Q: Evaluate the integral -6y dy e2y

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Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

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Q: * Lct X; ~ exp (2) · Show that T= EX, is Su fficient pro pesty of T %3D

A: How to find the sufficient statistic 1. Find the likelihood function 2. Apply the Neymann…

Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

A: 1. (a). To prove: ∫cschx=lnex-1ex+1+C Proof: We know that, sinhx=ex-e-x2 The left hand side can be…

Q: S az lnz (In z + 1)dz z In

A: ∫azlnzlnz+1 dz Put, z lnz=u⇒1·lnz+1z·z=dudz⇒lnz+1=dudz⇒lnz+1 dz=du

Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

Q: Show that * Ső› X yn+¹ J₁ (xy) dy=Jn+1 (x)

A: Using the recurrence relation of bessel function

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.