Compute the line integral of the scalar function f(x,y) = sqrt(1 + 9xy) over the curve y = x^3 for the domain of x between 0 and 8.

Q: (a) Express the mass M of a thin wire in 3-space as a line integral. (b) Express the length of a…

A: a) The objective is to express the mass M of a thin wire in 3-space as a line integral. The mass of…

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: Find Lebesque integral of function on segment (-3,0) 1 f(x) = %3D x+3

A: Given, fx=1x+35 Let, A be the set of all rational number in -3,0. Here, mA denotes the Lebesgue of…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Evaluate the integral. (Use C for the constant of integration.) / test at

A: We have to use byparts formula

Q: Use Green's Theorem to evaluate the line integral

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Q: .2 (3 – z)(3z + 1) dz

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Q: show the line integral is independent of path

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Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: Evaluate the integral using formula 35 (from the 1-page differentiation & integration formula) by…

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Q: Determine the following indefinite integral. Check your work by differentiation.

A: The given integral is Simplify the integral

Q: What change of variables is suggested by an integral containing V100 – x??

A: 100-x2

Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

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Q: Evaluate the line integral F.dr

A: In this question, we find the line integral for given vector function and parametric path.

Q: y' = 2 – 3xy; {-1<x<4, -4 < y s 4}

A: To plot direction field we plot small lines with slope calculated form differential equation after…

Q: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

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Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0)  and then to the…

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Q: Show how an improper integral having an integrand f(x) with a pole x0 is regularized as a…

A: Cauchy principal value, is a method for assigning values to certain improper integrals which would…

Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

Q: The path C is a line segment of length 5 in the plane starting at (4, 1). For f(x, y) = 4x + 3y,…

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Q: Explain how the substitution u = ax + b helps to perform an integration in which the integrand is…

A: ∫f(ax+b)dx, ax+b=uDerivative formuladdxxn=n xn-1

Q: Prove that the homogeneous integral equation

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Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: By making an appropriate change of variables, evaluate the double integral -y², I = || ( + y)e* v°…

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Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: Зх-2 dx%3D V2x+3

A: We need to evaluate the following integral I = ∫3x-22x+3dx                            ........1

Q: 1. Estimate the integral using Trapezoidal approximation rule with n=4: 2 + t)dt

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Make the given Differential equation in exact form and than integrate.

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: We will find out the required solution.

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: Set up an integral for the length of the curve. y = Vi-x7, -sxs 1/4 4+ 49, 12 dx -1/4 4- 4x7 + 7x6…

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Q: A cylindrical barrel of oil has a diameter of 1 meter and its sides are 2 meters high. Given that…

A: The objective here is to set up the formula to evaluate the work required to pump the oil over the…

Q: Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

A: Given information:- Find the work done in stretching a spring of natural length 8 cm, from 10 cm to…

Q: et dz V1-e2x

A: Given problem:-

Q: if Zcand Zp is complementary function Particular integral for the equation f(x X F(x,y) respectively…

A: This is Partial differential equation.

Q: Express the integral / rV1: V125 – 23 dr in terms of Beta function.

A: The solution is given as

Q: EVALUATE THE FOLLOWNG DOUBLE INTEGRAL BY REVERSING THE ORDER OF INTEGRATIC Vx²+! 'dx dy

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Q: Find the integral of the Ponction fiyリ=

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Sudv= 2x)dx can be evaluated using integration by parts of the form v=uv

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Q: State the Fundamental Theorem for Line Integrals

A: To State: Fundamental Theorem for Line Integrals Here we will use the knowledge of fundamental…

Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: A circular plate of radius 5 cm is immersed in a liquid of specific weight w such that its…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: It is not possible of an integral of a function to be zero over a contour although the function is…

A: Yes it is possible,