Use Green's Theorem to evaluate the line integral below. dx + 5xy dy C: r = 1 + cos(0), 0 s0 s 2n

Q: Evaluate the line integral by the two following methods. fwox xy dx + x²y3 dy C is counterclockwise…

A: Since, we have to evaluate the line integral given by:-I=∮C xy dx + x2y3  dy -(i)Our aim is to solve…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. S r xy dy dx dz 0,

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. x dz dy dx -6+x²+y?

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Q: Evaluate the iterated integral. 4 cos (x + y + z) dz dx dy /o Jo

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Q: Verify Green's Theorem by evaluating both integrals aM y? dx + x² dy = | / (G dA ay əx for the given…

A: Solved below.

Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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Q: Calculate the iterated integral. r5 CT/2 (y + y2 cos(x)) dx dy -5Jo 120

A: Given query is to find the value of the individual integral.

Q: Calculate the iterated integral. (x + y)? dx dy

A: The given integral is

Q: Evaluate the line integral along the given path. ²+ y? +z?) ds C: r(t) = sin(t)i + cos(t)j + 2k Osts

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Q: Evaluate the line integral , F dr where F (3 sin x, -5 cos y, xz) and C is the path given by r(t) =…

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Q: evaluate the iterated integral.

A: Evaluate: ∫-10∫-11 x+y+1 dx dy

Q: Calculate the iterated integral L So (y + y² cos x) dr dy A. 10 В. 13 С. 16 D. 18

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Q: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Evaluate the double integral f(r, 0) dA. 7 cos(8) r dr de

A: The given double integral can be evaluated as

Q: Calculate the line integral of h (x, y) = (2xy) i+ (x² – 2ry) j; over r (1u1) = cos u i+ sin u j, u…

A: Here,hx,y=2xy i + x2-2xy jr(u)=cosu i+sinu j

Q: 4. Evaluate the iterated integral by converting to polar coordinates. (a) f(x² + y²) dydk 0 (b)…

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Q: Evaluate the line integral by following the given steps. 4xy dx + 2x²y dy C is the triangle with…

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Q: Evaluate the line integral along the given path. C: r(t) = sin(t)i + cos(t)j + 3k osts 8

A: The given line integral is ∫Cx2+y2+z2 ds where c is a curve rt=sinti+costj+3k  and  0≤t≤π8.…

Q: Evaluate the iterated integral. /2 x. 4 cos (x + y + z) dz dx dy

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Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

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Q: 20. Re-write the triple integral =9 dz dy dx so that dV = dx dy dz, then evaluate the triple…

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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 Riemann-Stieltjes integral cos(r) da(r) where a(x) = E 2-"I(x – n-1).

A: Given:Integral ∫02cos (x) dα (x)where α(x) = ∑n=1∞2-nI(x-n-1)

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

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Q: Evaluate the integral b. 0 (z sin x + z cos y)dzdydx

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Q: Evaluate the double integral f(r, 0) dA. 2 sin(0) cos(0) dr de Sketch the region R. A/2 T/2 3h 2 1…

A: Evaluation of the double Integrals

Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: 2. Convert the integral In(r² + y? + 1) dx dy into a polar integral and then evaluate it

A: Explained below

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

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Q: Let p (x +e*siny) dx + (x +e* cos y)dy be the line integral on the boundary of the triangle enclosed…

A: To find the equivalent double integral we will use the Green's Theorem also we will draw the…

Q: Evaluate the iterated integral. 5 (T/2 r cos e dr de dz

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: evaluate the iterated integral.

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Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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Q: evaluate the iterated integral.

A: Given- ∫02∫-11x-ydydx To find- The value of the above integral.

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

A: Evaluate: i ∫252+u3uduii ∫ey1+eydy

Q: Calculate the line integral of h (x, y) = (2xy) i + (x² – 2xy) j; over r (u) = cos u i+ sin u j, u e…

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Q: Question attached thanks!

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Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

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Q: Consider the following. V2x - x2 x² + y? dy dx Convert the iterated integral to polar coordinates.…

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Q: Calculate the line integral of h (x, y) = (2xy) i + (x– 2ry) j; over r (u) = cos u i+ sin u j, u E…

A: Given function is  hx,y=2xyi+x2−2xyj To compute the line integral over ru=cosui+sinuj from 0 to 2?.

Q: Evaluate the iterated integral below. 1 S. * S'y cos 0 0 y cos (x) dy dx

A: Given, ∫0π4∫01y cos(x)dy dx

Q: Evaluate the iterated integral below. TL S. 1 *Sycos (x) dy dx 0

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Q: Let E {(x, y, 2) E R³ : 1 < x < 2, 1 < y < x², xy < z < 1}. Write the integral dV in the order dz dx…

A: Given,    E = (x, y, z)∈R3: 1 ≤x≤2, 1≤y≤x2, xy ≤z≤1Then ∫∫∫E dV =∫y=1x2∫x=12∫z=xy1 dz dx dy

Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy -3Jo

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Q: evaluate the iterated integral.

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Q: Evaluate the double integral f(r, 0) dA. -z/2 7 cos(@) r dr de

A: The objective is to evaluate the given double integral

Q: Evaluate the iterated integral 3 In z x e' dy dz dx

A: Given,         ∫13∫xx2∫0lnzxedydzdx

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 I T wy!! dy dx xy" dy dx 22 0,

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

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.