Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

Q: Find the antiderivative for each tunction When C=0. a) g(x)= -3x-4 b) nlx) = x-4 %3D c) Kl) =x42x+3

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Q: C. e3x dx

A: Given- ∫01e3xdx To Find- The value of the above definite integral.

Q: Sax²< x²-1)"dx s x5 JxZ Hl dx It zx

A: Use the algebraic substitution to evaluate the integral. Assume I=∫2x3x2−14dxLet…

Q: Q2) f(x,y) = 2xy x(s,t) = 3s-2t and y(s, t) = s²+4t. Find Je Je as at

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Q: Evaluate the Ś Ŝ (x²+2xY+ y% ) dy de when Step Size of xz0.2 and step of y=o.5 ? (use -> Trafezoi…

A: let f=∫01∫02x2+2xy+y2dydx with step size h=0.2 we have x0=0.2 , y0=0.5 fx0,y0=0.22+2×0.2×0.5+0.52…

Q: Name a secant. B. DF 2 回 [B] SY lal 32 [v] A

A: In geometry, a secant of a curve is a line that intersects the curve at a minimum of two…

Q: O Find The desivative of the following xy = 8 O y = 2re" © Cos (xy) = 4x² - 3y? 3D8 %3D 2. %3D

A: (a) xy=8 (b) y=2xey (c) cosxy=4x2-3y2

Q: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

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Q: = cos(x + y), when x = 0, y = " %3D

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Q: Use the substitutions : = ye S =X Q.3 to solve the du + y Əx PDE : %3D х, и(1, у) — сos y.

A: Using the substitutions we will solve for the PDE given as follows: ∂u∂x+y∂u∂y=x ∂u∂x+y∂u∂y=x…

Q: Select the best option based on the information below. MP at(x;,x;). = TRS = MP, %3D %3D - W2 Select…

A: Given....

Q: [AFE] Given, y = V1+ cos (x²) Find by using chain rule.

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Q: Find the general antiderivative. If the substitution method is used, state first u, du and [lu)du.…

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Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

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Q: Find Duf at P. f (x, y) = sin(4x - 4y); P(4, 4); u = j %3D NOTE: Enter the exact answer. Duf = %3D

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Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: EX show that J, (x) 2. sin X %3D zm + Sol:- J CX). = (-) M=D0 m+ LIN

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Q: Let y = eka, where k is constant. The values of k .1, –3 that make y" – y – 2y = 0, are %3D :Select…

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Q: Which of the following areas are equal?Justify your answer.

A: We can represent these areas by integration For first areas A1=∫01exdx For second areas…

Q: Using WXYZ from the previous question, if WY = 32, find XY. %3D

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: Find : b e R such that 81 / sin(b)y dS 10' whereSis the part of y? + z² 4 which is between x = 3 - z…

A: ∫∫Ssin(b)y dS=8110where S is the part of y2+z2=4 which is between x=0 and x=3-z in the first…

Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: The function y=4 sin z satisfies the IVP: %3D y" +y = 0, y(7) = 0, y (7) = -4. Select one: O True O…

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Q: F.ds, W by the pl

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Q: Evaluate dz using the given information. z = 8x2 + 3xy + 9y2; x = 1, y = -9, dx = 0.09, dy = -0.07

A: An equation can either be an identity, a conditional equation or a contradiction depending upon the…

Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: d. y =x (n* + e*)6

A: Given that, y = x (πx + ex)6 And we have to calculate the differentiation of the given function,

Q: (d) utt Q2: Use separtion of variables to find product solution for du 3 +x dy du

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Q: Given y = Vx3 + 1, evaluate dr using delta process.

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Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Find the value of the secant for ZR. 3)14 14 а. b. V5 с. d. 3 R O A

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Q: .3 dx J Tx²+9 .2

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Q: Given f(x, y) = 3x* cos (y), find COS fzy(x, y) = fyw (#, y) = | %3D

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Q: Sahving DES with Homagoneaus Coafficients 2 (2724 y?) dz- xydy- o esson:

A: Rearranging 2(2x2+y2)dx=xydydydx=4x2+2y2xy       =4+2y2x2yxLet…

Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: The antiderivative of Cos(3x) is Blank 1 (use small letter no space)

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Q: the solia generated Find the volumc af by revolving about the line X =3 the reg ion and y = x² + x…

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Q: 2xy" – y' + 2y = 0 about the point x = 0.

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Q: Evaluate: 3z dz when C: z = 0.5et (0 < 0 < T) %3D

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Q: AssIGN MENT2 : 2nel Order Homagenats ODE Egu 8 Fid geresal selution for ;- =0 | dx² dx y" -12 g'…

A: General solution for :   a)  y''+16y=0   Solution:                   This is the second-order linear…

Q: integrate the following:  Ue the U-substitution. ∫3/(√4x2-12x+9) dx

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Q: (2х — 3)- dx; и %3D 2х— 3

A: Given, ∫2x-3-7dx ;     We have to find the antiderivative using the substitution u = 2x-3

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: The colution oF y" + 16 y = 0 is y= C,cos 4x + C2 6in 4x. IF y C0) = 8 and y' (T/4) - 32, find…

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: Ex Find the Salution of the sliff. equ. + 2x° cosx, given that yf z dx

A: Here we have to solve differential equation