2 -2 + Q f(x) = 7x + x²-8x + 1 6 2 g(x)= R 135x² 3 2 + 4x + 2 6 x Let f and g be the functions defined by f(x)= x+²-8x + 1, and g(x) = -5² + 4x + 2. Let Q and R be the two regions enclosed by the graphs of fand g shown in the figure above. a) Find the sum of the areas of regions Q and R.

Q: A volume is described as follows: 1. the base is the region bounded by x = -y² + 6y + 119 and x =…

A:

Q: A volume is described as follows: 5 1. the base is the region bounded by y = 5 – a and y = 0 9 2.…

A: Volume of the region,

Q: A volume is described as follows: = 1. the base is the region bounded by x x = y² 18y + 92; 2. every…

A:

Q: The base ofa solid is bounded by the parabola y = 1 – x² and the x-axis. Find the volume of the…

A:

Q: The base of a solid is the region enclosed by the graph of y = vln x, the line x = e, and the…

A: Given,  The base of solid is the region enclosed by y=ln(x), the line x=e and the x-axis. Also…

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of f(x)=8-1-8),…

A:

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

Q: The base of a three-dimensional figure is bound by the y-axis and the curve x = + 2 on the interval…

A:

Q: Let the region R be the area enclosed by the function f(x) = 2x³ , the horizontal line y = –3 and…

A: Given the region R be the area bounded by fx=2x13,y=-3,x=0,x=3. Visualize the solid: Each…

Q: A volume is described as follows: 4 x² and y = 0 25 1. the base is the region bounded by y = 4- 2.…

A: Given the base region is bounded by y=4-425x2 and y=0. ymax=4-425x2max=4 From y=4-425x2 ,x = ±524-y…

Q: The volume of the surface generated by rotating the function f(x) (* > 1) around the x-axis is А. 2т…

A: The cylindrical shell method is used for calculating volume of revolution.

Q: x Let the region R be the area enclosed by the function f(x) = x² - 2, the horizontal line y = -3…

A:

Q: The surface defined by z = f(x, y) = 2x + y hovers above the region defined by the graphic below.

A: For the given surface  F(X,y)=2x+y The region bounded by curves is shown in figure  To find the…

Q: A volcano and z = x² + y² fills the volume between the graphs z = 0 1 ²+2), and outside the cylinder…

A:

Q: A rectangular plate is bounded by the x and y axes and the lines x = 6 and y =4. The thickness t of…

A:

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.