y = f(x) 2r cross-section y = g(x) base view The base of a certain solid is an equilateral triangle with altitude 15. Cross-sections perpendicular to the altitude are semicircles. Find the volume of the solid, using the formula V = A(x) dæ applied to the picture shown above (click for a better view), with the left vertex of the triangle at the origin and the given altitude along the x-axis. Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. The lower limit of integration is a = The upper limit of integration is b = The diameter 2r of the semicircular cross-section is the following function of x: A(x)= Thus the volume of the solid is V =
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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
