Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a unit circle centered at the origin. What is the value of the integral if we take a clockwise direction?

Q: Sketch the curve y cu. = x sq.   Use Formulas 3 and 4 to set up two integrals for thearc length from…

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Q: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8<x<π/8

Q: Use a double integral to find the area of the region. The region within both of the circles r = 6…

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Q: Evaluate the integrals in Exercises using integration by parts

A: The integration given to us is  ∫tan-1ydy            (1)

Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

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

A: Topic - length of curve using integrals

Q: Evaluate the integral / sin (9x? + 4y?)dA, where R is the region in the first quadrant R bounded by…

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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: Choose five other iterated integrals that are equal to the given iterated integral. r2 f(х, у, 2) dz…

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Q: Evaluate the iterated integral: S", Si yz dx dz dy.

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Q: 2. Evaluate each of the following line integrals in two ways*. F (x, y) = (2x – cos y) i + (x sin y)…

A: 2. (a) Directly: The equation of the curve C1 is x-4+y5=1( intercept form), or, y=54x+5. The…

Q: Choose z = x to transform the integral to a new integral in the variable z and evaluate the new…

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Q: Evaluate the integral (+ 2) dz where C is the line segment from the origin to the point 1+ 2i.

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4y dx -…

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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: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: fx=x3 is a polynomial function. It is continuous in the interval 0,3.

Q: Use an appropriate change of variable to evaluate the double integral: cos dA, R where Ris in the…

A: Given integral is  ∫∫Rcos(y-xy+x)dAR is the region bounded by x+y=1 ,x+y=2 in the first quadrant.

Q: Evaluate the line integral by the two following methods. $(x- y) dx + (x + y) dy C is…

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Q: Evaluate the double integral x cos y dA, where D is bounded by Y = 0, y = x², and x - 2. Answer:

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Q: DEvaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x 2. %3D

A: Integration of cos(x) = sin(x) Integration of sin(x) = -cos(x)

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: Sketch and evaluate the reverse integral 3. dy dz

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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: Evaluate the double integral y sin(2³)dA where R is the triangular region with the three vertices…

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Q: 14) ſe Vtanh® e" dy

A: Given that evaluate the integral

Q: Evaluate the double integral æ cos y dA, where D is bounded by y = 0, y = x², and a = 1. Answer:

A: Solve the following double integral

Q: Evaluate the line integral, where C is the given curve. ∫(with c in subscript) x sin y ds, C is the…

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate the integral starting from C of ydx + xdy+ zdz, where C is given by x=cost, y=sint, z=t^2 ,…

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Q: Evaluate the integral 8x cos y dy dr y – 4 by reversing the order of integration.

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Q: Evaluate the integral by making an appropriate change of variables. 9 cos( 3 (Y-X)) dA where R is…

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Q: 2y-ya Evaluate the integral 12 + y?dzdydr by using cylindirical coordinates.

A: Let z = z , x = r cos(theta) , y = r sin(theta).

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

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Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

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

A: First we have to plot region of integration.

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x – 9 In(x), 1sxs 4 dx

A: The integral for the length of the curve is  L=∫ab1+dydx2dx

Q: Compute the integral | x"dx, with a=1, b=7, and N=5. Answer to three decimals.

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Q: Evaluate the integral by making an appropriate change of variables. 7 Cos (3 (V=X)) d y + x 637 6…

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Q: Evaluate the line integral, where C is the given curve ʃc (x+9y)dx +x2dy, where C consists of line…

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Q: The line integral (23 (x° + y°) ds, where C is the arc of the parabola y = x2 from (0,0) to (2, 4),…

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Q: - SxS Write an integral for the area of the surface generated by revolving the curve y = cos (3x)…

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Q: Write an integral for the area of the surface generated by revolv-ing the curve y = cos x,…

A: The given curve is

Q: Evaluate the line integral, where C is the given curve. C is the arc the curve y = Vx from (4, 2) to…

A: We have to find the line integral of ∫Cx2y3-xdy, C is the arc of the curve y=x from (4,2) to (9,3)