9. Consider the region bounded by y = x2-4r+5 and y 2. The region is revolved about the y-axis to produce a solid. -3 -2 2 3

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: 4. Find the centroid of the region bounded by graphs of y = 4x – x², y = 2, and r = 0.

A: As per guidelines we experts are allowed to solve one problem at a time. Please reupload the fifth…

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

A:

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

A:

Q: 12. In the xy plane the region D is bounded by the lines y = 2x + 6 y = 2r +1, y = -3r +6, and y =…

A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

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

A:

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

A:

Q: 13. The volume generated when the region bounded by the curve x = /1+ y, the y-axis and the lines y…

A: Please rate

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

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

A:

Q: (a) Consider the region bounded by the graphs of y=c(2x-4), x-1, x-3. and y 0 where c is just a…

A:

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: THE REGION BOUNDED BY 2y = x AND (x-2)² = − 4y + 12 15 REVOLVED ABOUT THE LINE Y = 4. DETERMINE THE…

A: Introduction: The washer method refers to this application of the slicing method. Because the slice…

Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the…

A: As per company guidelines we are allowed to solve maximum three sub parts so i am solving first…

Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

A:

Q: could i please get help with 9a?

A:

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: 20 4 18 16- 14 12- 10- Y = (x- 2)4 6 - 21 2. 3, 00 4.

A:

Q: If the region under the graph of y = 3x +4 from a axis, then the volume of the resulting solid is 2…

A:

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

A:

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

A:

Q: ex The region bounded by the paroholm y =2, r the line y=1 in Hhe first quadrant bout the lin x=2 to…

A: .

Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

A:

Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

A:

Q: 12) Find the volume of the solid bounded by x² +y² = 4 and z=x+y in the first octant.

A:

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: 13. The region bounded by y = x°, y = 0, and x = 2 is revolved about the line x= 2. Find the volume…

A: Formula: The volume of the solid revolution generated by using disk method is given by,…

Q: Consider the region bounded by the parabolas x = 8y^2 and x = 5 + 3y^2

A: Given parabolas equation-x=8y2  ....(1)x=5+3y2 ....(2)Solve equation (1) and (2) we get…

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

A:

Q: ]]] xyz dV if S is the region bounded above by x² + y² +2²= 16 and below the S cone 2 = √² + y² with…

A:

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

A:

Q: Calculate the Pntegrals over the defined region . y=-2x and y=1-2x on paralleberaM clased with Rhes.…

A:

Q: Consider the following equations. 1 x² O 6 Sketch the region bounded by the graphs of the equations.…

A: The area of region R which is bounded by the curves f(x) and g(x) between the lines x=a to x=b and…

Q: 15. Find the volume of the solid enclosed by the surfaces 2 = 0 and 2-16-2-², whose projection onto…

A:

Q: PROBLEM [ B2 ]: Find the volume of the solid of reolution bounded by the circle z +y = 16, and the…

A: We have to find  The volume of the Solid of revolution bounded by the Circle x2+y2=16 and the lines…

Q: 11. Use the Shell Method to calculate the volume V of the solid obtained by rotating the region…

A:

Q: Evaluate |// e-V where E is the region between two cylinders z + = 4 and r +=9 with 1< y55 and : <0…

A: We will find out the required value.

Q: C. Find the volume of the solid obtained by rotating the region bounded by y = -10 + 6x-x², x = 1…

A:

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

A:

Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

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

A:

Q: 17. (2 +y +2) dx dy dz, W is the region bounded W by x+y+z= a (where a> 0), x = 0, y= 0, and z= 0.

A: We have to solve the integral and show the graph of question 17.

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: 2. Evaluate Vye"V dA where D is the region bounded by y = x² and y = 4.

A:

Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

A:

Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.