2. Sketch the region R enclosed by the triangle with vertices (1,0), (2, 1) and (1,1) and find the volume of the solid generated by revolving R about the y - axis. (Note: Use the variable of integration y)

Q: Find the average value of f(x,y) = x² + y² over the region R: rectangle with vertices (0,0), (2,2)…

A: Introduction:   A function f(x,y) average value as defined by favg=1A(R)∬Rf(x,y)dA   where A(R)…

Q: Find the volumes of the solids Find the volume of the solid generated by revolving the region…

A: The region is bounded by the curve y=sin x and the lines x=0, x=π, and y=2. The region is rotated…

Q: What is the volume of the solid below? (1, 1) y=x y=x R (0, 0)

A:

Q: Find the volume of the solid whose base is the region bounded by the z-axis, the curve y-√²+9.z 0…

A:

Q: R is the region bounded by the functions f(z) = 2+√z and g(x)=x-2 and the lines z = 0 and 2 = 3.…

A: Given f( x ) = 2 + x g( x ) = x - 2 from x = 0 to x = 3 line

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

A: Density: δ The region is bounded by x=y2-2y and the line x=2y

Q: m1. Subject :- Advance Math Find x coordinate of centroid of area bounded by y=1/root(4-x^2).…

A: The region is bounded by:, .To Find: x coordinate of the area bounded by the given region.

Q: Ris the region bounded by the functions f(x) = 2? +1 and the g(x) = – 2 and the lines x=1 and x=3.…

A: Given that  f(x)=x^2+1,g(x)=x-2 To find the volume of the region

Q: 4- Find the volume of the solid generated by revolving the region about y-axis,the region in the…

A: Draw the graphs of y=x2, x=2 and identify the region bounded by the curves. The required region is…

Q: Find the volume of the solid obtained by rotating the triangle (2,0)(2, 4)(1, 1) about the…

A: Solution :-

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 region de limited by S the sm face parametu zed by R(u, u) - sin (u) cos(v)i+…

A:

Q: find the volume of the revolution of the area bounded by y=4x-x^2 and y=3 rotated about the y axis.

A:

Q: The lamina area density p has the shape the equations, find mass (m). y = vx , y= 0, x = 3

A:

Q: The region Rin the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y = x² + 1.…

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.