Find the area of the region between the curve 1 6t = - e and the x-axis from t = 0 to 7 A) 7 x = et B) 9 t = In 9. |3D C) 8 D) 6

Q: Evaluate the double integral Sre+2vdA, where R is the triangle with verices (0,0), (2,0) and (2, 2).…

A: Introduction:  Integrals are the values of the function discovered through the integration process.…

Q: Use špheričal čoördiñatės. Evaluate tet dv, where E is the portion of the unit ball x2 + y² + z² s 1…

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Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: Hiw Enadunte SSS where s is the selid bounded the Śur faces

A: Given - S is the solid bounded by the surfaces x2 + y2 = z2, z = 0, z = 1 To find - Evaluate ∭Sx2 +…

Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: Evaluate the double integral. / 4x2sin y²dA; R is the region that is bounded by y = x³, y = -x³, and…

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Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Integrate the fallswingfuntinne aver the given regionr s R: the circle x+y=t and y=x? thiss

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Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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Q: Evaluate y xz dV, where Wis the domain bounded by the elliptic cylinder = 1 and the sphere x? + y +…

A: We need to evaluate ∭Wxz dV, where W is the domain bounded by the elliptic cylinder x29+y216=1 and…

Q: Exercise 11. Compute the area of the pseudo-sphere, i.e. the surface of revolution obtained by…

A: Area= ∫2πrds=2π∫r.dr/sin(ϕ)∫2πrds=2π∫r.dr/sin(ϕ) Due to tangent property: r/sin(ϕ)=a,r/sin(ϕ)=a, and…

Q: Let CR be the circle of radius R centered at the origin. Use Green's Theorem to find the value of R…

A: ∮ y3 dx+x dyUsing green's   theorem∮P dx+Q dy=∫R∫∂Q∂x-∂P∂y  dAP=y3                  Q=x∂P∂y=3y2…

Q: Let D be the region in xy-plane enclosed by the Trapezoid with vertices at the points (1, 1) , (7 ,…

A: We need to use double integral across given trapezium

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: Consider the parallelepiped with adjacent edges Find the volume. u = 2i + 7j + k v=i+j+7k w = i +4j…

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Q: By making an appropriate change of variables, evaluate the double integral = (x + y)e*-Y dxdy where…

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Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

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Q: 3. Evaluate JS Vr2 + ydA, where R is the region bounded by the circles with center (0,0) and radius…

A: (3) Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Prove that the area bounded by a simple closed curve C is given by | xdy – ydx. Hence, find the area…

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Q: Consider the region D in the xy-plane which is bounded by the following 2 -, Y = 4 y? = x and y' =…

A: Evaluate the integral in two ways. Directly and changing the variables. Last image is the shorter…

Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Consider the area of the part of the plane z = ax + by+C that projects onto some region D in the…

A: If the area of the region D on xy-plane is k. That is, ∫∫DdA=k. If the area of the some region of…

Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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Q: Compute the area enclosed by the curve r = Vsin 0 for 0 <o<T. O 1/2 5/2 3/2 O 1

A: Need to find area

Q: 4. Evaluate f, 2ry dA, where R is the region bounded by y i and

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Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: If the region R is bounded between two circles x2 +y? = 1 and x²+y? = 16 , then we have: J| x²+y?)…

A: Let's find.

Q: ryz dV if S is the region bounded above by 2? + y? + 2² = 16 and below the %3D 1² + y² with dV…

A: To evaluate the given integral, convert the Cartesian coordinates into spherical coordinates. Use…

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 the Cauchy integral formulas to evaluate the eiz cos z dz, 2²(2z – 37) where C is the region…

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Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

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Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

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Q: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

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Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

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Q: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.