Let F = ( ) and y = {x² + (y – 2)²) = 1 with anti-clockwise orientation. Find line integral , F. ds. %3D %3D

Q: Evaluate the iterated integral. LLL- 2 x³ y2 + z?dxdydz 0.

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Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here , we have given an integral and we have to integrate over a rectangle whose vertices are given…

Q: Evaluate the iterated integral. 24 (x + y + z) dx dz dy of

A: To find: ∫02∫04∫01x+y+zdxdzdy

Q: Calculate this integral a Sat-x? 3/2 x²+y²)¯ dy dx -a

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

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Q: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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Q: Evaluate the iterated integral. 21 V441-y у dx dy 21 441-y у dx dy %3D i

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Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Evaluate the line integral by the two following methods. pxy dx + x?y³ dy C is counterclockwise…

A: Sketch the graph of the triangle with vertices points (0, 0), (1, 0), and (1, 4) as shown below:…

Q: Calculate the double integral. JS y dA, 4xye+²y R R= [0, 1] × [0, 8]

A: Given; ∫∫R4xyex2ydA, R=0,1×0,8   As we know the common integral. ∫eax+bdx=1aeax+b+C  And ∬dA=∬dxdy…

Q: Consider the triple integral I = S S“(y² – 6z)dydzdx. -

A: ∫02∫x21∫0xzy2-6zdydzdx=∫02∫x21z3x33-6z2xdzdx=∫02x31-x812-6x13-x63dx=31.88888…

Q: Calculate the iterated integral a) (6xy² – 2r) dy dr

A: I am going to provide solution of 2nd question. Kindly repost the other one.

Q: Evaluate the triple integral S" S, sin y² dz dy dx.

A: We need to find the triple integral ∫03∫0π∫0ysiny2dzdydx. So,…

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

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Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

Q: Evaluate the iterated integral. TT V4 – z² z sin(x) dy dz dx

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Q: Evaluate the integral |/ x² dA by making an appropriate change of variables where a D D is the…

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Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

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Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

Q: (a) (x2 + y?) dx dy J2

A: To calculate the integral: ∫-11∫24x2+y2dx dy Solution: When we will integrate with respect to one…

Q: Evaluate the iterated integral. Tt/4 y cos(x) dy dx

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Q: Evaluate the iterated integral. (x + y²) dx dy THERE

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Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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Q: Evaluate the iterated integral. * T/4 y cos(x) dy dx

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Q: Evaluate the line integral along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

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Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 y…

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Q: Evaluate the integral: 2+u du a) b) / e"V1+ ev dy

A: Evaluate: i ∫252+u3uduii ∫ey1+eydy

Q: Evaluate the line integral, where C is the giv z² dx + x² dy + y² dz, C is the C

A: See the details solution in below

Q: Express the iterated integral in the opposite order. f(x, y) dy dx J7x/8

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Q: Calculate the iterated integral. 5xyV x? + y? dy dx

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Q: Evaluate the integral x2 ds where C is the portion of x2+y2=4 from (0,2) to (-2,0).

A: ANSWER:

Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t3, t2) for 0 <t< 3

A: Here, x=2+t-1 y=t3 z=t2

Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t³, t2) for 0 <ts 3

A: Given: From the above function, the following can be written,

Q: Evaluate the iterated integral. 24 V576-y у dx dy 24 V576-y2 y dx dy = i

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Q: Consider the following line integral. xy dx + x?y dy, Cis counterclockwise around the triangle with…

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Q: evaluate the iterated integral.

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Q: Calculate the iterated integral

A: The given double integral is  I=∫01∫04xy+ydx

Q: Evaluate the iterated integral. 5x (x + y²) dy dx J4x

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Q: Find the double integral by using for polar coordinate for ſf, (x2 + y²)3/2 dydx Where R:between y=x…

A: We have to evaluate the double integral by using polar coordinates

Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

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Q: Evaluate the iterated integral. V 4 - y2 (x + y) dx dy

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