Evaluate : //| cos(x² +y³) dV, where E is the region bounded by the disk x² + y? < 9 E and the plane z = 1.

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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Q: SSL. xy dV, where T is the first-octant solid bounded by the coordinate planes and the upper half of…

A: Here we have to find  ∫ ∫ ∫T xy dV , where T is the first-octant solid bounded by the coordinate…

Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: O (y +ev* )dx + (2x + cos y)dy , where C is the boundary of the region enclosed by the parabolas y =…

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Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

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Q: Evaluate the line integral by applying Green's theorem. 7xy dx + (x + y) dy, where C is the boundary…

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Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: Evaluate the surface integral I F. dS when F(x, y, 2) = y²i+ 3x² j and S is the graph of - ža (1+æ²…

A: Here, Fx,y,z=y2i+3x2jz=121+x2-y2

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

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

Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: e dV where E is bounded by the parabolic cylinder z = 1 -y and the planes Evaluate the triple…

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Q: Evaluate xy dV where E is bounded by the parabolic cylinders y = x², x = y² E and the planes z = 0…

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Q: Let æ = u cos (v), y = u sin³ (v) COOS (a) Sketch the region D in the xy-plane corresponding to 1 <…

A: Given that: Let  x=ucos3(v) and y=usin3(v) (a) Sketch the region D in the xy-plane corresponding to…

Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Let x = u cos³ (v), y = u sin³ (v) (a) Sketch the region D in the xy-plane corresponding to 1 < u <…

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Q: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

Q: Evaluate SSS z²dV, where R is the region given R by above the plane z=O and between the spheres 2. +…

A: A scalar function is a rule that is used to associate a number, or quantity with a particular point…

Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: Evaluate the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

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Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

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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: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

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Q: Evaluate the line integral f. y³ dx – x³dy, where C is the positively oriented circle of radius 2…

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Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: (1) Evaluate the double integral L V² + y² +1 dA where D is a quarter disk of center O(0,0) and of…

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Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: Evaluate (x + 5y) dV where E is bounded by the parabolic cylinder y = x² and the planes z = 3x, y =…

A: given is  a partial differential equation in dX , dY, dZ we can partially integrate the given…

Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Let R:x²<ys 3 be the closed region having boundary C with counter-clockwise orientation. F=[X…

A: We are given that the closed region R: x2 ≤ y ≤ x/3, is having boundary C with counter-clockwise…

Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: . Integrate f(x, y) = cos (x² + y²) (a) over the closed unit disk; (b) over the annular region 1 <…

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

Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: sketch the region described by the following cylindricalcoordinates in three-dimensional space. 0 ……

A: The given region is  0≤r≤3-π2≤θ≤π20≤z≤rcosθ   Sketch this region in cylindrical coordinates as shown…

Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…

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Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

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Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

Q: Use Green's Theorem to evaluate the line integral (y +eva) dx + (2x + cos y²) dy , where x2 and C is…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.