True or False. 1. If one uses the horizontal strip/element as a representative area, then the infinitesimal change may exist in either x or y variable depending on the orientation of the curve. 2. If a polar equation r = f (θ) is made θ = f (r), the limits of integration r1 and r2 must be obtained from the corresponding values of θ1, and θ2 which bound the area of concern. 3. The point (-13, -110π/4) is located between 0 and 1.80π region of a polar coordinate system and is identical to (13, 3π/2). 4. For any rose-petal curve in the form r = a cos(nθ) with the same maximum length a, the equation with the greater number of petals m, (m= n for odd, 2n for even) will always yield to larger area of the curve. 5. Any polar equation can be made rectangular. 6. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for as long as the centroid of the figure and its distance from the axis of revolution are given. 7. The shell method is most applicable for cases when the area to be revolved is some p(y) distance from the axis of revolution.
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.
True or False.
1. If one uses the horizontal strip/element as a representative area, then the infinitesimal change may exist in either x or y variable depending on the orientation of the curve.
2. If a polar equation r = f (θ) is made θ = f (r), the limits of
3. The point (-13, -110π/4) is located between 0 and 1.80π region of a polar
4. For any rose-petal curve in the form r = a cos(nθ) with the same maximum length a, the equation with the greater number of petals m, (m= n for odd, 2n for even) will always yield to larger area of the curve.
5. Any polar equation can be made rectangular.
6. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for as long as the centroid of the figure and its distance from the axis of revolution are given.
7. The shell method is most applicable for cases when the area to be revolved is some p(y) distance from the axis of revolution.
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