.rdx dy Prove that (a) (b) (8)

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: If z = e'x + y In(x), find z, and z, Zx Zy II

A:

Q: In Evaluate the integral: ₁²t² fln s t teu du ds dt

A:

Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

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Q: is given by Oxy = E(XY) HxHy.

A:

Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: dy de Xoy. -Secxy)

A:

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

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Q: Evaluate the integral. 7y°dy y'-9 7y dy y7-9

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Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: Evaluate the integral. Ay'dy 4y'dy y- 12

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Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

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Q: If the têst is inconclusive, then say SO. 3* Σ k! k=1 If p = +o, enter "inty". i

A: Given query is to find series converges or diverges.

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

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

A:

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: Evaluate the integral: S S. 4 dx dy 0 y? 294 3 196 3 392 3 98 3

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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: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: Apply Green's Theoren to evaluate the integral. C6x+y) dx + (3xy"+4y) dy ter

A: Given integration is ∮c(6x+y3)dx+(3xy2+4y)dy C : Any simple curve in the plane for which Green's…

Q: S dy 7 y2-8y+5

A:

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: 2.Prove that L (sinwt) %3D s2+w?

A:

Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: S 1.Prove that L (coswt) = %3D s2+w2

A:

Q: 2. Evaluate the following integral: dy dx

A: We need to reverse the order of integration to calculate given double integral

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

A:

Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

A:

Q: Fand the anti daniahir of fw. e+e- 2Cosed px -

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Q: n of eY dydx ? 0.

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Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: Evaluate the integral. dy e8y

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Q: x2 1 dr dy = a° In(1+ x² + y? 3

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Q: dy is then da In a If y = cosh r

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Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

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Q: 4. Find path integral J xdx+ ydy, if L is the segment: x-1,y= and re (0.1]

A: Given x=t, y=t2, t∈0,1

Q: Evaluate the integral. yz dx dz dy O8 68 3.

A: We have to evaluate the given integral

Q: lx)にX sit. ors<I prove that inl Guernesto uniterady. Guveryes to

A:

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

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Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: Oprove Heed A A lnda = 2 - - where feass integmle even funchen

A:

Q: Evaluate the in tegral (x+ 2y) dy

A:

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Q2: Evaluate the integral fx In x dx using by parts formula

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Evaluate the double integral : re dy dx 4

A: Given,          ∫1e∫467xdydx