10. Consider the double integral JR 1+x²+y²' ху dxdy. (a) Evaluate the integral where R is the triangle with vertices A(1,0), B(5,0), C(7,3). (b) Evaluate the integral where is the unit circle with center D (5,–1)

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. C:…

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Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

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Q: 8. (8) In each part, write an integral (do not evaluate, but simplify the integrand) to find the…

A: Surface area about x axis formula is  S=∫ab2πy1+dydx2dx Given y=13x3 Find out dy/dx by taking…

Q: S, (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Use Green's Theorem to evaluate the line integral. 3x2eY dx + eY dy C: boundary of the region lying…

A: GREEN'S THEOREM:

Q: AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: Verify Green's Theorem by evaluating both integrals an am dA ax ay for the given path. C: rectangle…

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Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: Evaluate the line integral J xe" dx +y sin y dy along the triangular path consisting of the line…

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Q: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

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Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz - Calculate the…

A: Let's find.

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

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Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(r) 1 In r %3D where 1<r <…

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Q: Use Green's Theorem to evaluatc the integral x²ydx + xydy where C is the rectangle with vertices (0,…

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: 5. SKETCH the area D between the lines x = 0, y = 3 – 3x, and y = 3x – 3. Set up and integrate the…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

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Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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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: 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: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

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

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Q: 2. Identify u and dv for finding the integral using integration by parts. In(3x)dx а. u = In(3x)dx.…

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Q: 4. Use Green's Theorem to evaluate the line integral: f ye dx + x*y² dy, where C is the from (-2,0)…

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: Show that the line integral is independent of path and evaluate the integral. integral C…

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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: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: 11. Use Green's Thm to evaluate the line integral if the curve C consists of 3 line segments, from…

A: Solution:-

Q: Verify Green's Theorem by evaluating both integrals ON [ v² dx + x² oy - [√(x 0 ) A dy = dA JR əx ду…

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Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

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Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: dl /x² + y² + 4

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Q: If the curve y= from (0, 0) to (3,9) is rotated about the x-axis, the integral that represents the…

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Q: d) Use line integral method to evaluate F(x, y)• dř ,where R 1 F(x, y) = (3x y°i + 4xy² j) and M, N,…

A: The graph of curves y=x2, y=x is as follows The yellow colored region is region R

Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.

Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…