6. Evaluate ffſ z² dx dy dz taken over the volume bounded by the surfaces x2 + y² = a?, x² + y² = z and z = 0.

Q: Find the volume generated if the area bounded by curve y = x^2 and the line y = 2x + 3 is revolved…

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Q: 3. Find the volume of the solid bounded between z = I and the region D, where D is the area bounded…

A: The solid formed is as follows: The region D in xy-plane is as follows: The curves intersect at…

Q: Set up an integral for the volume of the solid S bounded by the x2 + y2 - z2 = 2, and z = + 3

A: The definite of the volume element will result in the volume of the solid required. The definite…

Q: 5. Find the volume generated by revolving the area under the eurve y = e from x = 0 to x = 1 (a)…

A: Given problem is :

Q: Given a solid bounded by f (x, y)= 2x2 + 4y", xy-plane, x= 2, x= 10, y = 5 and y = 14. If the order…

A: We will find out the required value.

Q: 2. Find the volume under the surface f(x,y) = y In x over the rectangular region R = [1, 3] x [0,…

A: We will find the volume using double integral.

Q: 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x %3D 2…

A:

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-…

A: Solve by using graph

Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

A:

Q: The volume generated when the region bounded by y = x , y = 1, x = 0 is rotated about x - axis is…

A:

Q: Sketch the region R whose area is given by the iterated integral. 16 – y2 dx dy 3 2- 2 6 8. 10 12 14…

A: option B

Q: Set up the integral to find the volume obtained by rotating the region contained in9 = y = 1, and ax…

A:

Q: by rotating Find the Volume oF the solid obtained bounde d by und X=4 y=o rotating y= 8 on

A:

Q: The volume of the solid under the plane 3 x+ 3 y -z=0 and above the region enclosed 23 by y=2 x and…

A:

Q: 5. Find the volume generated by revolving the area under the curve y = e from x = 0 to x = 1 (a)…

A:

Q: D. Calculate volume enclosed by (z = 8-x² - y²) and (z = x² + y²), (Use order dy dz dx). وكنت طول

A: Given

Q: SI xyz dW, B is region bounded by two cylinders, wwwm w В x^2 + y^2 = 16, x^2 + z^2 = 16, and the…

A: Consider the given volume of the two intersecting cylinders given by  x2+y2=16 andx2+z2=16  as shown…

Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

A:

Q: The volume generated when the area of the finite region enclosed by the x-axis and the curve y = x –…

A: Given curve is y = x-x^2

Q: If R is the region bounded by y = x* – 1 and y = -x² – 1, find the volume V(S) of the solid S…

A:

Q: Find the volume generated if the area bounded by curve y=x^2 and the line y=2x + 3 is revolved about…

A:

Q: 3. Consider the region bounded by the y-axis, y = V3x + 1, and r = 4. Set up an integral to compute…

A:

Q: please set up the integral and find the volume. thankyou

A: The equation of cone with x axis as the axis of cone, is x2=y2+z2, |x|≤1 It is bounded by the planes…

Q: Compute the volume bounded by y=x2-2x and 3y + 2x?-27 = O when it ís revolved around the y-azis. A.…

A: Note: According to our expert guidelines only first individual question is to be answered.kindly…

Q: Find the volume obtained by revolving about 0X the area under the catenary y = (a/2)^(e^x/a +…

A: Find the volume.

Q: Set up the integral that gives the volume of the solid enclosed between the curves y=1/2x, x =2, x=4…

A:

Q: Evaluate the double integral Jl, x dx dy where the region R is bounded by: 3 y = 4x – 3, y =x +, y =…

A:

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k? = 0 and…

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line…

Q: 6. Evaluate ffS z² dx dy dz taken over the volume bounded by the surfaces x2 + y? = a?, x² + y² = z…

A:

Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

A:

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

A:

Q: Set up the equation in solving volume of the solid generated when the area bounded by x = Vỹ, x = 0,…

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: - Find the volume of the solid that is bounded above by the cylinder z = 4-x2, on the sides by the…

A:

Q: Evaluate the triple integral. III. 7z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

A:

Q: 12. Set up an integral to find the volume of the solid generated when the vegion bounded by y=…

A: Giveny=x  , y=o , x=4

Q: 1. Find the volume under the parabolic f(x,y) = x²+ 4y² and above the rectangle R :0 < x < 1,1 < y <…

A: Given  fx,y=x2+4y2

Q: 5. Find the volume generated by revolving the area under the rve y = e² from r = 0 to x = 1 (a)…

A: y=e^x

Q: Set up the integrals to find the volume generated by revolving the region bounded by y 4 – 2x and y…

A:

Q: Set up the double integral that solves for the volume of the solid bounded by the cylinder x² + y? =…

A:

Q: 4. Use a triple integral to find the volume (set up and evaluate). z = V1 - x² – y² r = sin 0

A: As r=sinθ, then x=rcosθ=r1-sin2θ=r1-r2y=rsinθ=r2 The limits of integration are…

Q: Evaluate the triple integral. III. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the…

A:

Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A:

Q: and a) x = y² + 1₁ x = 0, y =- y = 2 The volume generated by revolving the region about the line y=2…

A: We can solve as follows

Q: Evaluate the double integral ∬DxcosydA,∬Dxcos⁡ydA, where DD is bounded by y=0,y=0, y=x2,y=x2, and…

A: To evaluate the below double integral Here D is the region bounded by y = 0, y = x2, and x = 4.

Q: Evaluate the triple integral. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

A:

Q: The integral represents the volume of a solid of revolution. 2T X° dx

A: Use the principle of integration to evaluate the given problem.

Q: 5. Find the volume generated by revolving the area under curve y = e from z = 0 to z = 1 (a) about…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.