Problem no. 1: Determine the following: Given the area bounded by the curve y? -x and the line x = 4. What is the volume generated when this area is revolved about the x-axis? The following methods can be used to solve for the volume generated - (i) Disk (ii) Ring (ii Shell -. What method/s is/are applicable for this problem? Which of the following is a point of intersection?• O i and ii O (-4, -2) O i and i (4, -2) ,i and i O (-4, 2) O None of the above (2, 2) O None of the above What is the volume, in cu units, of the solid generated? * O 2pi Which of the following statement is TRUE for the curve y^2 = x? 4pi O The curve is a parabola whose vertex is located at the origin and opening to the left 8pi The curve is a parabola whose focus is located at the origin and opening to the right 16pi The curve is a parabola whose vertex is located at the origin and opening upward O None of the above The curve is a parabola whose vertex is located at the origin and opening to the right None of the above O O O o O O O O O O
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.
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