Find the area of region enclosed by x = t – t", y =t – t°, 0 < t < 1 using Green's Theorem.

Q: Use Green's Theorem to evaluate the line integral. y? dx + xy dy C: boundary of the region lying…

A: From Green's theorem, ∫CMdx+Ndy=∬∂N∂x-∂M∂ydydx If M=y2 ;N=xy, then ∂N∂x=y ; ∂M∂y=2y

Q: Use an iterated integral to find the area of the region. dy dx = y 8 7 5 4 3 2 1 -1 1 4 -1l 3. 2.

A: We need to setup and evaluate integral.

Q: Prove that: I = , Cos () dxdy = sin(1) 2 where R the region bounded by x + y = 1,x = 0,y = 0

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Q: Find the area of region enclosed by x = t - t", y =t – t, 0<t < 1 using Green's Theorem.

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Q: Use a line integral to find the area of the region R. R: region inside the loop of the folium of…

A: This is a problem of the area inside a loop of Folium.

Q: Find the area of region enclosed by x = t – ť², y = t – t", 0 <t < 1 using Green's Theorem.

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Q: Use an iterated integral to find the area of the region. y = 25 - x2 dy dx = y 25 20 15 10 5 1 1 2

A: The equation of the curve is given by y = 25-x2 The graph of the region is  To evaluate: The area…

Q: Evaluate the double integral / (3x + 2) dA I D when D is the bounded region enclosed by y = x and y…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given: ∫Cy2 dx+xy dy, where C: boundary of the region lying between the graphs of y=0, y=x, and x=25…

Q: Evaluate the double integral. 7xy dA; R R is the region in the first quadrant enclosed by y = Vx,y =…

A: We have to find the ∬7xydA

Q: The double integral J 2xy dA over the rectangular region R= {(x, y) E R, 0<x<4 and - 1<y<0} is equal…

A: Consider the given integration as ∬2xy3dA And given limit as 0≤x≤4 and -1≤y≤0

Q: Find the area of region enclosed by x = t – t“, y =t – t°, 0 <t < 1 using Green's Theorem.

A: The solution are next step..

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

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Q: Evaluate the triple integral I = y dV where D is the region in the first octant (x > 0, y > 0, z >…

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Q: Find the area of the region (as shown) in two ways. a. By integrating with respect to y. b. Using…

A: a). Required area is,

Q: 4/ Math

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

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Q: Calculate the integral/ / (x + y)* sin° (x – y) dA, where D is the region given by D = {(x, y) : |+…

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Q: Use Green's Theorem to evaluate the line integral. | y? dx + xy dy C: boundary of the region lying…

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Q: What is the value of the double integral Y – x sin |dA, y+ x where R is the trapezoidal region with…

A: Here we have to find the value of the given double integral ∬R sin{(y-x)/(y+x)} dA, where R is the…

Q: The double integral ff 2xycosydA over the rectangular region R = {(x, y) E R?, 0< x<1 and 0 <y<n}is…

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Q: Find the area of the region bounded by the spiral r = 0 for 0 <0 <T. (77, 7)

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Q: Find the integral ∭U(x2+y2)dxdydz, where the region U is bounded by the surfaces x2+y2=3z, z=3.

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Q: Use Green's Theorem to evaluate the line integral. √ y² dx C: boundary of the region lying between…

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Q: Use an iterated integral to find the area of the region. dy dx = y 10 9 8. 7 6 5 4 3 2 1

A: As we know that; The equation of the line when it passes through the points x1,y1 &amp; x2,y2…

Q: Evaluate the integral [(*+y+z)dx dy dz. over the tetrahedron bounded by the planes x=0, y-0,z=0 and…

A: Given

Q: 3. Use a suitable change of coordinates to calculate the integral / x² – y² dA, where R is the R…

A: The region R is given by

Q: Sketch the region R and evaluate the iterated integral ffa (12x+4y) dy dx Ја Јахо f(x, y) dA.

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: Find the value of integral / F dr, where C is the semicircle parameterized by F(t) (cost, sin…

A: In F put value of x and you in terms of sin and cos then take dot product and use integration

Q: 3. Use a suitable change of coordinates to calculate the integral /| 1² – y² dA, where R is the R…

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Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: Evaluate the moment M, and My of the region bounded by x- 2y - y? and the y-axis.

A: Given area is bounded by x=2y-y2 and y-axis.  On the y-axis, x=0. We try to find the point of…

Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: Sl, Cos () dxdy sin (1) Prove that: I = JJ. x+y where R the region bounded by x+ y = 1,x = 0,y = 0

A: Here we have to prove that       ∫∫R Cos{(x-y)/(x+y)}dxdy = sin(1)/2  Where R is the region bounded…

Q: find the area of the x+y+z= 6 plane part remaining in cylinder x2 + y2 = 6

A: The area of the plane, z=f(x,y) remaining in a surface is calculated by the formula below .…

Q: integrate ƒ over the given region. ƒ(x, y)  = y cos xy over the rectangle 0&lt;= x &lt;= pai, 0…

A: Given, f(x, y) = y cos( xy ) and we have to calculate integrate this function over the given region.

Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: Evaluate SI, cos (2) dA ,where D is the region bounded by (x, y) D = {- sxs V24 ,0 < y< x²} V8n

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Q: a.) Find the area of the surface defined by 4x + 2y + z = 1, x² + y? < 1. b.) Evaluate the integral

A: Surface area

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: Evaluate the double integral /VA- y? dA, R where R is the region bounded by the circle x² + y? =

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Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Find the value of integral F dr,where C is the semicircle parameterized by F(t) - (cost, sin…

A: We calculate the given integral.

Q: Consider the inetgral | (5x + 18) dA where Ris the region between the circles a2 + y2 = 1 and a2 +…

A: Consider the integral ∬R5x+18dA where R is the region between the circles x2+y2=1 and x2+y2=4. The…

Q: Use Green's Theorem to evaluate the line integral. v? dx + xy dy C: boundary of the region lying…

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Q: . Find the area of the region enclosed by the loop of the curve x = 1 – t², y = t – t³ at a pol

A: Solution: The objective is to find the area of the region enclosed by the loop of the curve x=1-t2…