(1– y°)dx+(x° +e )dy, where C is the boundary of the region between the circles x2 + y2 = 4 and x2 + y2 = 9, positive orientation.

Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: S.(2x° +5y )dx+(2x-4y') dy C:boundary of the region lying between the graphs of x² +y² = 16 and x +y…

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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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: Evaluate I = , dx dy where R is the region that lies inside the circle x2 + (y – 2)2= 4 and outside…

A: We have to find ∬Rdxdy where R is the region that lies inside the circle x2+y-22=4 and outside the…

Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: Use Green's theorem to evaluate f, xy?dx + 3 cos ydy where C is the boundary of the region in the…

A: Let R be a region in the xy-plane that is bounded by a closed, piecewise smooth curve C, and let…

Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…

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Q: The integral ∫C[(3x2y+y2)dx+(x3+2xy)dy] is independent of the path. Evaluate the integral where C is…

A: Given: R=ti+(t2+t-2)j   for 0&lt;=t&lt;=2

Q: |(x+2y)d4, where D is the region bounded by the parabolas y=2x² D and y =1+x.

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Q: (a) Find the solution of the limit using polar coordinate system. x² + y2 lim (x,y)-(0,0) x2 + y?…

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

Q: Evaluate fpxV47x² + 47y² dA, where D is the shaded region enclosed by the lemniscate curve r? =…

A: To find the value of the double integral         ∫∫Dx47x2+47y2dA where D is the region enclosed by…

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

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Q: The circle of radius 3 centered at the origin Ex. to calculate the area of the given region.

A: Given: The region between x-axis and the cycloid parametrized byr(t)=t-sin t, 1-cos t  for 0≤t≤2π

Q: Given the path C that is the line segment from (-4; 0) to the origin, and the curve y = 2x² from the…

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Q: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

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Q: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

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Q: Use Cartesian coordinates to evaluate [[[ ²² y² dv D where D is the tetrahedron in the first octant…

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Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: (1- y*)dx + (x° + e*)dy where C is the boundary of the region between the circles x² + y² = 4 and x²…

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Q: Q3/ Evaluate: 1- SS (4x + 2) for the region enclosed by the curves y = x² and y = 2x 2- Show that…

A: 1. Consider a function of two variables, z=fx,y. The double integral of function fx,y is denoted by…

Q: Given (1 + y³)y' = x². (i) Determine a region of the xy-plane for which the given differentia…

A: Explanation of the solution is given below...

Q: By using polar coordinates, evaluate the double integral -y²dx dy x² + y² over the region in the…

A: Answer is given using polar coordinates.

Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: Evaluate o y dx – x³ dy, where C includes the two circles of radius 2 and radius 1 centered at the…

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Q: (b) ( y cos(ry) dA over the region R = {(x, y)|0<x < 1 and 1 < y <7/3}

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Q: dA, where R is the trapezoidal region Cos 5. Use appropriate change of variables to evaluate x + y,…

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Q: Given: f(x,y)=x-2y+3 and D is inside x +y =16 and to the right of the y-axis. Write the integral K =…

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Q: Q:3: a) Find the surface area of the object obtained by rotating x=e2y, -1sys 1 about the y-axis.

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

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: b. $ (xy2 + sin(x + y?)) dx + (3x²y + 2y sin(x + y2))dy where C is the clockwise boundary of the…

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Q: By a suitable change of variables, evaluate ſf, dx dy where D is the region in the first quadrant…

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Q: Sketch the region enclosed by the given curves. y = 3D 4 cos(5x), у %3D4 —4 cos(5х), 0 < x < T/5

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Q: Find the area of the surface generated by revolving the right-hand loop of the lemniscate r^2 = cos…

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Q: Evaluate the line integral f. 4y dx + z² dy + (16 – x²) dz over the quarter of the circle of radius…

A: To Determine: Evaluate the line integral over the quarter of the circle of radius 4 in the xz-plane…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = -x2 -…

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Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: 7 sin(æ), æ = T, I = 27 and The region R in the first quadrant of the xy-plane is bounded by the…

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Q: Зу + 7eV X + 7ev x) dx + (10x + 7 cos(y?) ) dy C is the boundary of the region enclosed by the…

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Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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Q: In the figure to the​ right, the equation of the solid curve is y equals StartFraction secant…

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Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

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Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: I = Examine the given integral dz ;C z-i -|= 2 the circle

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Q: sin y 11- nY dA where D is the region bounded by the curve y = vx and the line y=x, if y # 0

A: try not to ask multiple question at a time. solve double integral

Q: O Find the area of the region enclosed by the ellipse x = a cos t, y = b sin t, 0<t< 2n

A: Since you have asked multiple questions in single request.so we will answering only first…

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.