In r dy If y , then is cosh z

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

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Q: 1 Prove that 3 dx s VI VI

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Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

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

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

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Q: use the definition prove that s d sinZ %3D Tal

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Q: - Evaluate the iterated integral 3xyz dz dy dz.

A: Definition. • In calculus, an iterated integral is the result of applying. integrals to a function…

Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: dy de Xoy. -Secxy)

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Q: Evaluate the integral. * m/6 cos(z) dz sins (z) Jn/2

A: Given,          ∫π2π6coszsin5zdz

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: 25-x² dx In if we let u = V25 – x , then udu =-xdx.

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Q: To start the integral fx/1+x® dz, we let u= O 23 O 26

A: We use substitution to simplify the integral.

Q: 19. f' "'In rdr r'In r dr

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Q: Show that F(n fla)] ds pleae do it frast

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

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Q: 4 ∞ dy dx J I+ 4? 2. 00

A: To find the integration

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: The DE : y = e-/Y is seperable Select one: O True O False on

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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: O prove that : (2) DO 2x e dx a e +b where a, b >o

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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: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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

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Q: If u= In x, then 1- (In x)2 dx=?

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: . Explain how you woułd prove the following. Given: HY = LY; H F WH || LF Prove: AWHY = AFLY

A: Given that HY≅LY  and WH ∥LF We have to prove that △WHY≅△FLY   When a transversal line intersects…

Q: If dx = In |x| +C, then d 및 (In |x| + C) = for x> 0. X

A: Given,         Assuming that x>0, use differentiation to justify the formula ∫1xdx=lnx+C.…

Q: To prove that 2 dx 1+ (In x)2 + In x+c = 2 In %3D X1 + (In x)2 we use the substitutions U = Inx then…

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Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: 1. Find fr fy and fry if f(x,y) = y* + x?y + In xy.

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Q: Jy cosy smy dy 3

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Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: 7 the n ya In Cx? _y?) Do not Equatio InCx-yリ Do not check modificd Laplace

A: This is a problem of partial and Laplace.

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

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Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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

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Q: If u In x, then 1-(In x)2 dx =?

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Q: he integral dx こ [in(x)]? x[In(x

A: Given integral is ∫1x(1nx]2dx let’s find the value

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

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Q: 3 Prove Prive that d tin'u e I du

A: As we now the identity tan2(x) +1=sec2(x)

Q: e? If u= In x, then 1- (In x)2 dx=?

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Q: In Evaluate the integral: Sto st² sin s teu du ds dt

A: The given integral is: I=∫12∫tt2∫0lnsteududsdt   The Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: 8) The integral |4* dx is equal to 5x 5x 5x - +C C. In 5 А. -+C In 4 В. +C 5in4 D. +C 4 In5

A: Given ∫45x dxSubstitute u=5x → dudx=5→dx=15du=15∫4u duNow solving ∫4u duApply Exponential rule: ∫au…

Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: Prove,J w' Sin wx du %3D COSZ 2

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