Find the volume of the solid of a revolution bounded by the graphs of f(x) = – x² + 5x – 4 and y = 0 rotated about the y-axis. V =

Q: Find the area of the “triangular” region in the xy-plane that is bounded on the right by the…

A:

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

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 ordinate of the centroid of the region bounded by the parabola y = -x2 and the line x = 2y…

A:

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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 centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 56. Use the…

A: The region is bounded by the graphs fx=x2 and gx=-x+56. We have to find the centroid of the region.

Q: enclosed betw parabola y = x2

A:

Q: The curve y = sqrt(x2 + 1), 0<=x<=sqrt(2), which is part of the upper branch of the hyperbola…

A: Find dy/dx from the given curve using power rule and chain rule.

Q: Find the center of mass of a thin plate of constant density 8 covering the given region. The region…

A:

Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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: 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: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

A: Given that a thin metal wire in shape of a semicircle occupies the curve , where  is the top half of…

Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

A:

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

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.