Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

Q: e3arcsin2x -Calculate the V1-4x2 integral

A: To evaluate : ∫e3arcsin⁡2x1−4x2 = ∫e3sin-1⁡2x1−4x2 Let , I= ∫e3sin-1⁡2x1−4x2 Substitute sin-12x = t

Q: U V3-22- zt

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Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: Q1 - Evaluate the following integra iv. a 1 2 x3Vx2-1

A: Given:   ∫22 1x3x2-1dx

Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4- 3.…

A: Given:

Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

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Q: Evaluate L.(x +y)dxdy by reversing the order of integra

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: The integrand Vx² + 64b², b > 0 , after substitution, becomes: x2 + 64b² %3D

A: Here we replace x by some variable so it makes our integrand easy to solve.

Q: 4. Evaluate f VX /xVX+ 1dx using integration by algebr substitution.

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Q: 9. √√4-4x² Convert ₁42(4-4x² - y²)dydr into a triple integral with dV = dydzdx. C

A: Given :∫-11∫-4-4x24-4x24-4x2-y2dydx and dV=dy dz dx To convert the double integral into triple…

Q: Consider the following integral 3dx V(16 + 4.x2 )5

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: D (x) is not integrable on [0,1]

A: Note: Here we are solving 1st problem for the next problem please submit the question again. Given:…

Q: To integrate by u-substitution, which part of the integrand should you choose as u? SG) · 2ª · In 2…

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Q: (a) Solve the line integral yzdx - xzdy + xyzdz on a particle that moves along the line segment from…

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Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: 9. i Convert S²₁ 4²(4-4x² - y²) dydr into a triple integral with dV = dydzdz.

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

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Q: Evaluate the integral 3e2x 2e-2x 1 In vZe-2x + /2e-4x – 3 +C 2/7 - 2x 2/3e2x - 2e-2x+C -등 Arcsinl…

A: Explained below

Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine…

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Q: Evaluate the iterated integra x2y dx dy o Jo

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Q: Use a substitution of u = r to integrate : dr.

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Show that A and AT have the same nonzero singular values. How are their singular value…

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Q: O Set up integrel for the Velume aboud x. 3 X= Y-2

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Q: Show that f(x) = x² is integrable on [a,b].

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Q: Consider the following. dz 4z + 2 1 Find a substitution to rewrite the integrand as du. 4u du = dz

A: Given : ∫dz4z + 2

Q: Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane…

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Q: Calculate the double integral. SSR 6x / 1+xy dA, R = [0, 6] × [0, 1]

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Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Evaluate the integra 7/t dt 7/t dt = t2 %3D

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: Estimate the error if cos vt is approximated by 1– in the integral J cos vt dt. 2' 4! 6!

A: For the given  Cos t = 1-t2+t24!-t36!+.... error is estimated as shown below

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=3,…

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Q: What is the integrable form of dr? 1 -1) du -u?) 2 du 2022-01..

A: Find the integrable form by substitution method

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: find the volue of the od specify ingrol integrol T-x2 the

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Q: Evaluate the integral: æ V81 *Vs1 – z'da -

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Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

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