3 FIGURE 13 Graph of S(x, y) = 16 – x² – 3y² R = [0, 3] × [0, 1].

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

A: 80π

Q: Find the abscissa of the centroid of the region between the parabola y = 5 − x2 and the line y = 1 −…

A:

Q: Find the volume of the se

A: Given, the curve                   y2(a+x)=x2(a-x)

Q: y=x2-2x+1 and y= -x2+2x+7   Use washer method to find the volume of the solid whih is obtained by…

A:

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: Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.

A:

Q: enclosed betw parabola y = x2

A:

Q: Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2,…

A: We have to find the area of the ellipse  x2+8xy+17y2≤1. Use the change in variables s=x+4y and t=y…

Q: 3. Region R is a first quadrant region bounded by f(x) = x?, the y axis and the line y = 4. The…

A: Use volume formula

Q: Find the volume of the solid of revolution created when the area bounded by f(x) = 2e-² (shown in…

A:

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: Find the center of gravity of the region between the graphs of y = x + 2, y = -3x + 6, and y =…

A: We have to find the center of gravity of the region bounded by

Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

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.