2). 3rin y l dy dx [ 5 X In Xナ3

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: 3-If u(x),v(x) and w(x) Find d/dx of (uvw)

A:

Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

Q: 7. Evaluate the Integral S (x + 3) dx

A:

Q: 2 al S ex+y dydx

A:

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

A:

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: 5 (show resulting de) 2xdx - dy=x(xdy - 2ydx) When: x= -3 , y = 1 %3D

A: Differential equation and it's solution

Q: In 2 ety dy dx In 3 1-

A:

Q: In 8 In y e**y dxdy S S Q2. Evaluate 1 0

A:

Q: Find dy/ux of the following 1)lf y = 1/ (1-u) and u = 1/ (1+x)

A: Given y=11-u and u=11+x

Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

A:

Q: 1 1 The integral x²dxdy represents the 0, area under the curve y = x² between x = 0 and x = 1.…

A: Given integral is ∫01∫01x2dx dywe know that ∫ab∫cd f(x,y) dx dy represent areaonly when f(x,y)=1

Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

A:

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

A:

Q: FIMD dY IF x= AMD Y= U 1tu3

A: Let's find.

Q: 21.14 Evaluate the following double integral: (x² – 3y² + xy') dx dy -2 Jo

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: 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: In(3) e Ver +1 dx In(2)

A:

Q: S dy 7 y2-8y+5

A:

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: Evaluate the following integral. 2 5 e 2,2 dz dx dy -221

A: Given: ∫-25∫25∫1ex2y2zdz dx dy ⇒∫1ex2y2zdz=x2y2∫1e1zdz       ...constant out⇒x2y2lnz1e…

Q: Evaluate the integral: S(6 + 5x) dx dy 22 44 O 4 O 2

A: Double integration

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

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

Q: 1. (a) Prove the following. | (In x)"dx = x(In x)" – n (In x)-' dx

A: To prove that 1.a. ∫lnxndx=xlnxn-n∫lnxn-1dxb. Using 1.a compute the following      ∫lnx3dx

Q: 3 Evaluate the gwen tri ple in legral. xsiny dy dz dx

A: Order of triple integral dydzdx

Q: In 13 Iny ex+y dx dy. Evaluate the integral 1

A:

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

A:

Q: 57 Evaluate the integral |[xy dy dx. 12

A:

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

A:

Q: x2 1 dr dy = a° In(1+ x² + y? 3

A:

Q: 1 uate the improper integral dx. x(In x)3

A:

Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

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

A:

Q: -64- Eke n Calcul afe th udlue of Z.Z ?

A: according to company rule we answer only first question and rest can be reposted.

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: In(v¤) dædy 6. 15. Calculate ry

A:

Q: find: Seos nit dt findo S sinnat at

A:

Q: (b) Evaluate In(x) dx 1

A: The given integral is divergent.

Q: 2 Evaluate: J. sov?sy cosx³dy dx

A:

Q: 2 1. Evaluate the integral: dx 2 x2-x

A:

Q: S √x²-a² X dx

A: To solve the given integral.

Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

A:

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: 3. Evaluate S, 2y²sinxy dy dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A: