(b) Show that the area bounded by y? = 4ax %3D and x? = 4ay is 10 a2. 3

Q: Find the area between the graph of y = x - 6x + 8 and the x-axis from x = 1 to x = 3.

A:

Q: Find the area included between x + y* = 4x and y = = x above x-axis.

A: Consider fx and gx be two functions between a,b and fx≥gx .Then area between graph of these two…

Q: the area between z=0  and z=-1.95 is

A: It is given that the z-scores are 0 and –1.95.

Q: A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line…

A:

Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Find the area generated by the graphs y=x4-2x2 and y=2x2

A:

Q: Find the area under the curve 2x+3y-6%3D0 from x+63D0 to x-19%3D0

A:

Q: Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis

A: We have to find the area bounded by the curves.

Q: Solve the area bounded by the parabola y2=4x and the line y=2x-4 in two ways. Graph it

A: We are given the parabola y2=4x and the line y=2x-4 .

Q: find area, y=2x , y=3-x2  (0,1)

A: Area is a 2-dimensional quantity which is the measure of amount of space covered by any shape in a…

Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

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.