5 / 7 129% + Question 18. Consider the function g(x) = sin²x, in the interval [0, 7]. Use the Trapezium Rule, dividing the interval (0,7) into strips of equal width d = 1/2, to find an estimate for the definite integral g(x)dx. Answer: Question 19. A circular area of re is swept out as a rod of fixed length r= 1 m pivots about a point through an angle of 0 radians. If area is increasing at a rate of m? per second, find the rate of increase of the angle 0 in rad/s. Enter your answer correct to 2 decimal places without units. Answer: Question 20. The arc of the parabola y = x² from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulting surface, considering that the formula for the surface area of a body of revolution around y axis is as follows: (dy` dx S= 2nx1+| dx.

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A:

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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.