Evaluate the integral along de given curve C.   C is the straight segment form (1,0,-2) to (4,6,3)

Q: а. Find the integral of e42 dz, where C is a circle z-2= 8 and x 1+ last digit of your ID.

A: In the given question we have to calculate the integral I=∮Ce4z(z-x)6dz where C is circle z-2=8 and…

Q: Compute the line integral 는 (J Where c is the part of Aheecrele xh ayt=g in the first quadrent from…

A: We will evaluate the given line integral.

Q: 4) Compute the integral where is the closed chrve SRe (z²)dz -2

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Q: Evaluate the integral using appropriate substitution. an V3- a de + C

A: It is required to evaluate integral by substitution.

Q: dz 2 t´ + Zz-3

A:

Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

A:

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: Calculate the following line integral where C is the straight line from (1,2) to (4,7). S xy ds C

A: The given integral is I=∫Cxy4 ds where C is the straight line from (1,2) to (4,7). We have to find…

Q: Set up, but do not evaluate the integral for the length of the curve.

A: We know that length of curve y=f(x) from x=a to x=b is given by

Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

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Q: Evaluate the integral. dA, R = [0, 6] × [0, 16] x + 1

A:

Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: Use Green's Theorem to find the integral rdy - dr where C is the curve consisting of three line…

A: Given integral is: ∫Cxdy-ydx

Q: 3.2. Prove directly from the definition of Itô integrals that t t | B?dB, = B - | B,ds .

A: The answer is given below

Q: Calculate the integral $dz, where C: |z] = 2.

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Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

Q: 1 dr. J =(1+ Inz)

A: Given indefinite integral is ∫1x(1+lnx)dx. Apply method substitution to solve the integral. Put…

Q: Compute each of the following line integrals. (a) / x ds, where C is the portion of the parabola…

A: We have to find the value of ∫Cxds where C is the portion of the parabola from 0,0 to 1,1,followed…

Q: Calculate the iterated integral 2 So Só Væ + ydædy

A:

Q: (b) Evaluate each of the following line integrals: (1) xds, where C is the portion of the curve x…

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Q: Evaluate the following line integral (x + y)ds where C consists of line segments from (0,0) to (9,…

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Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: Evaluate the line integral, where C is the given curve.  ∫(with c in subscript) (x + yz) dx + 2x…

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Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

A: where are is the trapezoidal region with vertices(8,0),(10,0),(0,10), and (0,8).

Q: (a) Calculate the following integral along the given path: where C is the straight line segment…

A: Note: As per Bartleby's guidelines, for more than one question asked, only one question has to be…

Q: Evaluate the line integral given in the figure below

A: Given question is belongs to the vector calculus and from the line integration we have to integrate…

Q: Set up and evaluate an integral that represent the length of the curve. x=r-r', y=p",15 4 3/2 3 4.

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Q: The value of the iterated integralS, L (3 - ry)dydx=.. 2

A: Given: ∫-24∫013-xydydx

Q: SJcos (In x) dx Evaluate the integral

A:

Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

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Q: Evaluate the integral, if C is the circular path y = (1-x^2) from (1,0) to (0,1).

A: Let y=1-x2 be circular path from (1,0) to (0,1). Parameterize the above path by taking x=cosθ , then…

Q: Evaluate the following line integral along the curve C. ds, where C is the line segment from (1,1)…

A: Using line integration formula

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x - 3 In(x), 1< x < 4 4 dx

A: The given curve y=x-3 ln(x), 1≤x≤4

Q: 14) ſe Vtanh® e" dy

A: Given that evaluate the integral

Q: Find the line integral of f(x,y,z) = x+ y+z over the straight-line segment from (2,1,3) to (1, –…

A: Solution: f(x,y,z)=x+y+z

Q: 9. Evaluate the integral, where C is the above half of the circle = R from z₁ = 1 to z₂ = -1.

A:

Q: Evaluate the integral

A: Solution Given ∫01x2(1-x2)52dx We need to evaluate the integral

Q: (8) Evaluate the contour integral: 2021 e1/z² dz. Izl=2

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Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

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Q: Evaluate the double integral | 3xydA where Ris bounded by y=2– x, y=0, and x =4 –-y² in the first…

A: this problem is related to application of integration

Q: 4. Use Green's Theorem to evaluate the line integral: f ye da + ay? dy, where C is the from (-2,0)…

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Q: Evaluate the iterated integral. T/4 '3 '3-r rz dz dr de

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Q: Evaluate the integral over curve C. f(x, y) = x + y, C : x 2 + y 2 = 4 in the first quadrant from…

A: Given, the curve                      f(x, y)=x+y,    C: x2+y2=4 in the first quadrant (2, 0) to (0,…

Q: Find the integrals. a) R= %3D R.

A: First we have to plot region of integration.

Q: z · 3°dz

A:

Q: Evaluate the integral: (In z)6 dz %3D

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Q: 22 Calculate the value of the integral over the following C curves, a) C:|2+1| = 1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: