2 If In(ax)dx = 2, then a = 1 O None e3 es 4 4) 4. 4.

Q: 5). S 13+1)E dx (Improper Integral)

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

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Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1

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Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: 2 If In(ax)dx = 2, then a = 1 es 4 4. O None e3 4. 4

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Q: みm 'cU24onba buimoll ut anos Give answers occurate to o tu100yら19 SONe the foilowing tigures 6.8=…

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Q: et Calculate the integral: dx (e – 4)(e* + 5) -

A: Given,            ∫exex-4ex+5dx

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Q: A. Find dy/dx of the following. 1. y = e" + eVinx + 2 In(ex) 2. y = er" 3. eln 4x + eln 4y = e + e"

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Q: if M Z- Sin (xy) fined 4 22 y= lint t-1

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

Q: Show that S, (In x)? dx = e – 2

A: The detailed solution is as follows below:

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

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Q: 2 If [ In(ax)dx = 4, then a = 1 es 4 O None eo 4 e4 4 4

A: Basics of Integration are used.

Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

Q: 20. In(e**) = e2iny A. = - D. = dy В. dx dy dy С. dx dx у dx

A: Given equation is ln(ex^(2))=e2lny

Q: 3.Evaluate ex dx, by Simpson's ½ rule. n=6` 1 = (b − a) ƒ (xo) + 4f (x₂) + 6 f(x₂)

A: We have to solve by Composite Trapezoidal Method.

Q: Integrate 2 In(11æ) -dx . O a) In (11æ)² + C 2 O b) , In (x)² '2백 + C 11 c) In (11æ)² + C 2x d) None…

A: Given query is to eveli the integral.

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: 25 - x2 In dx , if we let u=V 25 – x2 , then udu = - xdx. A True B False

A: On solving this we will get

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

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: S°1- (In x)2 dx=? If u= In x, then e A B L (1- u)du .2 © (1-u²)du

A: Given: I=∫ee21-lnx2xdx   ....1

Q: Evaluate: S ndy 2y+3 (y 1)(y 1) In G) ny² + y + 1| - arct arctan 0 Inly 1| ž(y 1)* nVi y arctan( ) c…

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Q: 2 If [ In(ax)dx = 4, then a = 1 es 4 O None e6 4 e3 4

A: e^5 / 4

Q: حالة إكمال الأسئلة السؤال 5 In dx= .a O .c O .d O 346I JS Kásl "übbUI JS báa" ġgå jäilg - Jluujllg…

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Q: 2 If [ In(ax)dx = 2, then a %3D 1 e4 4 None es 4 4 4

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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

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Q: In 4 In 5 e2X+ Ydy dx = 0 1 (Type an exact answer)

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Q: ht mLE)<o. o show fon My f, gn-",g fon Jn Mg fog that O Is m(El <a∞ necessary?

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Q: 1.) Evaluate In 2 e*2arctan e* 1.)J1+e2x) sec(2arctan e*)" dx

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Q: What will be the value of (h, k) in the given DE: * (x – 2y + 1) dx + (4x – 3y – 6) dy = 0 | h = 3,…

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Q: 1. Find b such that |(a) In 3. dx is equal to х (Б) 3.

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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: 1.) Evaluate In 2 e*2arctan e* A.) Jū+e2x) sec(2ªrctan e*) dx

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Q: In(v¤) dædy 6. 15. Calculate ry

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Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

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Q: Given that 1 dx = and x2 dx = , compute the integral. x dx = 4 2' 3' La - 20?. (1 – 2x)³ dx

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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: In csch 4y d 3) tanh 4y

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Q: s) sohne rec'x pecy dx + sing dy = 2

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

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Q: Integrate 2 In(11x) -dx . a) In (æ)? 2 11 + C b) None of these c) In (11æ)² + C 2 d) In (11æ)² + C…

A: topic - indefinite integral

Q: 1 (In(11) xy e*y² dxdy

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Q: 1. Evaluate a dV where E = {(x, y, 2) E R³ | 0 < z < x + y,0<x < y?,0 < y< 1}.

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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…