Evaluate the triple integral. JIJ 2xy dv, where E is bounded by the parabolic cylinders y = x² and x = y² and the planes z = 0 and z = 5x + y

Q: Use Green's Theorem to evaluate the line integral § 2y² dx + 3x² dy, where C is the boundary of the…

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Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Calculate the line integral F. dr, where F (3y, -3z, 2x + 2) and C' is the boundary of a triangle…

A: We will find line integral by using stokes theorem .

Q: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: Find the surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the…

A: The object is obtained by rotating about the x-axis over the interval .We have to find the surface…

Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: Evaluate the line integral (2x-y+6)dx + (5y + 3x - 6)dy, for which the path C traverses C around a…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Compute the line integral: y² dx + x² dy two ways. C

A: We have an line integralTo evaluate the line integral by two methods (a) By  Green theorem(b) By,…

Q: enclosed betw parabola y = x2

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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Q: No. of integral points lying inside the parabola y² = 8x and circle x? + y? = 16 are %3D (A) 15 (B)…

A: To find  The number of integral points lying inside the parabola y^2=8x and the circle x^2+y^2=16.

Q: Find the area of the plane z 2y + 5z = 13 cut out by the cylinder x² + y² = 9. area=

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: Use Green's Theorem to evaluate the following integral Let² dx + (9x + 5) dy Where C is the triangle…

A: We have to evaluate  where is the triangle with vertices  and .

Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3