Evaluate So y? exy dA, where D 'is bounded by you, yit, x

Q: Evaluate he integral isin (x+rJl dx

A: given integral, I=∫03π/2sin(x+π) dx we have to evaluate given integral

Q: The contour of integral zdz of the cirle |z-i| =2 is

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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: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Verify the Green's Theorem to evaluate the line integral . (2y²dx + 3xdy),

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Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x > 0

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Q: Prove from the definition of the Ito integral that sdW, = tWt – | W,ds.

A: To prove the below statement using the definition of integration. ∫0tsdWs=tWt−∫0tWsds

Q: Evaluate the impropec integral oc sho that it diverges, dx

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Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: 3)Evaluate /y² + 1dA , Ris bounded by x = 4 - y² ,x = 0 R

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Q: H.W where or is the selid bounded the Sur faces

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Q: Evaluate the double integral. // (x2 + 2y) dA, Dis bounded by y = x, y = x³, x > o

A: To evaluate the below double integral ∫∫Dx2+2ydA ,   D is bounded by y=x, y=x3,x≥0

Q: Obtain the moment of the area generated by x = 2a, bounded by x =y and x2 = 2av.

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Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

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Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Evaluate the integral. *T/2 csc t cot t dt 31.

A: 31. we have to evaluate the integral∫π6π2csc(t)cot(t)dt

Q: Ex(ia)g prove or dis prove that Ris equivalance relation on x iff Rtis equivalene relakion ony

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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: Find all Integers a so that the area enclosed by the lines y=ax,y=0 and x + 2y-4=0 is a natural…

A: To find: All integers a so that area enclosed by the lines y=ax, y=0, and x + 2y-4=0 is a natural…

Q: Find the integral ∮F • dR around the circumference of the circle x2 - 2x + y2 = 2, z = 1, where F =…

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Q: Evaluate the double integral.18. , D is bounded by y = x, y = x3, x ≥ 0

A: To evaluate the double integral. Given that  D is bounded by y = x, y = x3, x ≥ 0. We can define…

Q: Use the Fundamental Theorem of Calculus to find the area under curve of c)= 6z 4 13 between I=14 and…

A: Given function: f(x)=6x+13 Definition: Fundamental theorem of calculus: It states that f is…

Q: Evaluate the integral ∫sec z tan z/√sec z dz

A: Given: I=∫secztanzseczdz for evaluating given integral, in given integral we substitute secz=t…

Q: Let X,y EIR. Prove that if 21 x +35 y = 45 then x and y are not both integes.

A: Given: Let x,y∈ℝ. To prove: If 21x+35y=45, then x and y are not both integers.

Q: Evaluate the double integral where D is the triangle bounded by the x-axis, y-axis and the line y =…

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Q: Let f : [a, b] R be a function defined by 0if rEQ . if r¢Q f(x) = %3D Show that f is not Riemann…

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

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

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Q: Integrate f(z) = counterclockwise around the unit circle, usin %3D 28 – 9.7 - Cauchy's integral…

A: Given function is fz=1z8-9.7 and the contour is the unit circle oriented counterclockwise.

Q: Suppose that f(x, y) = = y√x + 1 on the domain D = Then the double integral of f(x, y) over D is […

A: Given function is f(x,y)=yx3+1 and domain is D=x,y 0≤y≤x≤3 We need to find the double integral of…

Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: let X = * = zrs, find 22u in term f partial deriva bives

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Q: 2) Let C denote the positively oriented boundary of the square whose sides lie along the lines x =…

A: Given line x=-2,2 &y=-2,2 is can be  solve as follow

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: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x2, x = 7 %3D

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Q: Evaluate the double integral + 2y) dA, where D is bounded by y = x, y = = x°, and x > 0. 3 Answer:

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Q: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: Evaluate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x 2 0

A: Consider the following graph:

Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

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Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

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Q: Compute the line integral of f = x? - y, along C:x² + y? = 4 in the first quadrant from (0,0) to…

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