Consider solid obtained that the region bounded by the lines  x = 0, x = 6 - y   , and y = 3. Sketch the region and sketch a slice that is perpendicular to the y-axis. Find the area function of the slices A ( y ). Integrate A ( y ) to determine the volume of the solid.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y =r°,…

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Q: Find the volume of the solid that results when the region enclosed by y = Vr, y = 0, and r = 81 is…

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Q: x^2 + 5x - y = 6; y = 0; x = 3

A: Please see the attachment  According to the guidelines we are supposed to do one problem.

Q: Revolve the region bound by y=x2+1,y=1-x and x=1 around by x-axis.

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Q: Determine the volume of the solid generated when the region bounded by the curve y² = x³, x = 2 and…

A: The region bounded by the curves y2=x3 and x=2, can be shown by the following image : If we put x=2…

Q: Calculate the volume of the region bounded by the spherex + y² + z² = 9 from above and by the cone…

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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.