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

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: 50.) Show how to use a line integral to find the area of a circular disk of radius r

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Q: tan (x) sec²(x) dx.

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

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Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

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Q: By using double integrals find the area between x = – y², lines y = x – 4, y = -2 and y = 2.

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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: show the line integral is independent of path

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Q: Evaluate the improper integral

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Q: Use an improper integral and information from Exercise 21to find the work needed to propel a 1000-kg…

A: From Exercise 21:

Q: Сompute 1. f dx, where f(x)=|x|.

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Q: Evaluate the integral of xydx from x =3 to x=6 when x = 6cos angle and y=2cos angle

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Q: evaluate the definte integral 4 at the top and 1 in the bottom square root of y+1

A: Given,         The integral 4 at the top and 1 in the bottom square root of y+1.

Q: By converting the integral I- rdrd® into Cartesian coordinates, we get:

A: Here we will assume coordinates for converting polar to cartesian. x=rsintheta y=rcostheta…

Q: Find the complete integral of (1 az 1 dz z dx2 1 az Exe z dx3 z dx *Ex 7x Ix =|

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Q: Evaluate the double integral S ry° dydx

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: (०हागो 10,3,0)and (0,0,6). Tongular lamina with for of stokes deo theorem.

A: Given

Q: Evaluate the line integral F.dr

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

Q: Set up the double integral in rectangular coordinates to compute the area of the surface z = x2 +…

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Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Calculate the integral   ∫6dx

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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: ZA So ydz + zdy+ ædz (3,4, 5) C , C2 (2,0,0) y (3,4,0)

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Q: Write expressions for the area enclosed by a curve interms of line integrals around .

A: Green's theorem transforms the line integral around C into a double integral over the region inside…

Q: | (In(5æ)) (In(5x))²dx

A: We use the by parts method ∫(ln(5x))2dx…

Q: x$ - Inx dx

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

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

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Q: COSz Show, without evaluating the integral, that z2(z + 1) *26 5 zp-

A: Given integral is , ∫ccoszz2z+1dz. Cauchy residue test: ∮fzdx=2πib1. Where b1is residue of fz.…

Q: Evaluate the integral (show clear work!): xsin x dx

A: Use formula of integration of parts method

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…

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Q: + 1 -оу-х -oy=x2

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

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

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

Q: Use double integral to find the avea l2: of the regien (4, 3) 3. -

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Q: Evaluate the integral. Snip

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Q: 1 Oblicz d.x, Vax ах — х2 – x²

A: In this question, we have to evaluate the improper integral. Here we also use the property of Beta…

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: Calculate the iterated integral.

A: First integrate wrt y then x

Q: Evaluate the lino integral y+ + (4+2-x>y +2が Where C consitts of line segments from 0,-,2) to…

A: