show the line integral is independent of path

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: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: What is the Fundamental Theorem of line integrals?

A: Our Aim is to define Fundamental Theorem of line integrals

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

A:

Q: I need to evaluate the follwing integral or state that they diverge

A: The given integral is ∫02dxx3

Q: The Green's Theorem allows us to replace any line integral over simple, smooth, closed curve in…

A: Yes, Green' Theorem allows us to replace any line integral over simple smooth closed curve in 3D…

Q: dx Vitex

A:

Q: sec sec |tar xp xp Suea () 2asS

A: We put sec(π/x2)=u and differentiate both sides with respect to u .thus we get du and value of…

Q: Illustrate the setting up limits of a double integral?

A:

Q: Сompute 1. f dx, where f(x)=|x|.

A:

Q: ate the integral. S sinx

A:

Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

A: Cauchy’s Integral Theorem : If f(z) is an analytic function in a simply-connected region R, then…

Q: What is the moment of inertia of the area bounded by the curve 2x^2 + 2x - y - 2 = 0 and the line y…

A: Image is attached with detailed solution.

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: integral

A:

Q: Explain the meaning of the surface integral in the Divergence Theorem.

A:

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: sec =zydy

A: Given

Q: State whether it would be quicker to evaluate this integral using horizontal lines (i.e. first along…

A:

Q: Use local linear approximation to estimate In (0.99

A:

Q: what is integral

A: Topic:- Calculus

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: Evaluate the iterated integral: dydx.

A: Definition used -                                                                       Where…

Q: – 4V5 )ds]

A:

Q: Write the correct iterated integral using horizantal Cross - sections y=3x y=x? ..

A: First we find limit of x and y.

Q: Find the area bounded by axes and line 7x + 5y = 35 using any differential strip

A: Explained  below...

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

A:

Q: Evaluate the integral. sec do %3D

A: According to guidelines we are supposed answer only first question if you want any particular…

Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

A:

Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…

Q: Evaluate the line integral S. 4x²ds, where C is the line segment from (-2, –1) to (0,–1) followed by…

A:

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

A:

Q: State the Fundamental Theorem of Line Integrals, including all required hypotheses

A:

Q: Evaluate the integral.

A:

Q: Use Stokes Theorem to choose the correct integral to evaluate the line integral

A:

Q: The improper integral 3dx is /1->

A: Given:⇒∫013dx1-x2⇒3∫11-x2dxWe know that ∫11-x2dx=sec-1(x)

Q: segment from ( 0,3,0) to (1, 3,7).Use line integral and check answer by caleulating (s.y.)

A:

Q: Show that the curved integral does not depend on the path joining its points and find the integral…

A:

Q: YA y= f(x)

A:

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: How to calculate the pseudo-surface integral from a line? Please explain it in your multivariable…

A: How to calculate surface integral from line?

Q: I need to evaluate the integral by reversing the order of itegration

A: Given,

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,