Use geometry to calculate (without integraung). o V16 - x2 dx Note that f (x) = v16 – x² is the top semicircle of %3D - radius 4.

Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: 2 1. Evaluate 8x" dx by the Gaussian quadrature method. 7

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Q: Evaluate ∫ 2xex dx using integration by parts with u=2x and dv=ex dx. Give only the function as your…

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Q: Integrating Factor by Formulas: (7) xy³dx + (x²y² + 1)dy = 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q3/A- Using Trapezoidal rule ,choose the correct integration value of S sin(2x) with width=15?…

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Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

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Q: ential equati x²y dy = C

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Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

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Q: Differentiate the function. y=(4x-4)° (3-x)? dy dx

A: Given query is to find the derivative of the expression.

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: Evaluute the integra dx 0 16+49x2

A: Here we have to evaluate I=∫-∞∞dx16+4x2

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: (3x? + у?)dx — 2хydy %3D 0

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Q: xdy – ydx – Vx²-y²dx = 0 хау — %3D

A: We have the equation xdy-ydx-x2-y2dx=0 This can be written as  xdy=ydx+x2-y2dx⇒dydx=y+x2-y2x We need…

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: (y5 – x²e») dx dy -11-3

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Q: x'dx √√x(1-x)

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Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

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Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: 9. Find the most general antiderivative; verify your answer by differentiation. a) f(x) = 2x*-Sx + 7…

A: a) on doing integration we get =2x^4/4-5x^2/2+7x+c this is the anti derivative of given function  on…

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: Use Taylor's formula at the origin to get a cubic approximation of the function: f(x,y) = ln(2x + y…

A: Given function f(x,y)=ln(2x+y+1) and a,b=0,0 Taylor's expansion  at origina,b=0,0 to get a cubic…

Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Q4. Test for exactness and solve (ycosx – cosy)dx + (sinx + xsiny)dy = 0

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Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

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Q: Q3/8- Using Simpson's rule ,choose the correct integration value of x* +5 ,with width = 2? =1030…

A: By Applying Simpson's 3/8 rule.with widht =h=2

Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Differentiate the function. 1 y3= (2x +3) dy dx

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Q: y

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Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx