II. Find the area bounded by the curve y = x3 - 3x and the x-axis. Sketch the curve indicating the area bounded.

Q: Find the area bounded by the curves y2 = 4x 4х + у — 6 %3 0

A: We need to find the area bounded by the curves y2=4x4x+y-6=0

Q: Find the area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: Find the area between the curves. y = x2 and y = - x2+18.

A:

Q: Find the area enclosed by the x axis and the curve y= 4-x2

A: Find the area enclosed by the x axis and the curve y= 4-x2

Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

A:

Q: Find the area bounded by the given curves. y = 3x2 and y = 27…

A: Given:

Q: Find the area between the curve y=4x-x² and the x-axis

A:

Q: Find the area bounded by the curve y=4x-x? and the lines x=-2 and y=4.

A: The given equation forms a downward parabola.

Q: Find the area bounded by the curve a^2y = x^3, the x-axis and the line x = 2a

A:

Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: 6. Calculate the area enclosed between y=x-4x2 – 5x and the x-axis.

A:

Q: Find the area between the CUoyes y=9-x² and y= -5

A: For any two curves f(x) and g(x) which intersect at points with x-coordinates a and b and bound a…

Q: (a) Find the area bounded by the curves y = 2x2 and y = 4x.

A:

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

A:

Q: Q- Find the area of the region bounded from the right by the curve x = 4 - y? ,from the left by the…

A:

Q: Determine the area bounded by the curves y = 6x − x2 and y = x2 − 2x and illustrate an accurate…

A:

Q: Find the area between the curves. x = -2, x = 4, y = 3e3x, y = 2e3x + 1

A: The above question is from the application of the integration part and since the major part of…

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

A:

Q: Find the area of the infinite region in the first quadrant between the curve y = eX and the x-axis.

A: Given curve, y=e-xand x-axis Formula for the area of the region under a curve is given by A=∫aby dx

Q: Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

Q: Find the area bounded by the given curves. y = 8x3 + 7 and y = 8x + 7 _________ square units

A:

Q: Find the area enclosed by the curve y = x 2 − 3 and the line y = 2x

A:

Q: Find the area between the curve y = x – and y = -x + 10x2 – 24x 10x + 24x

A:

Q: Find the area bounded by the line x-2y + 10 = 0, the x-axis, the y-axis and x=10.

A:

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9.

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.

Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: Find the area bounded by the curve y = 9 – x2 and the x-axis.

A: Area

Q: Find the area between the curve and the x axis over the indicated interval. y=8/x; [1,7]

A: We will use integration to find area under the curve

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

A:

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

A:

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A:

Q: Find the area in the second quadrant bounded by the curve y = x' +4x² – x – 4 and the x – axis.

A:

Q: Find the area bounded by the given curves.y = x2 − 3 and y = 12 − 14x2…

A: First we graph the curves using graphing calculator.

Q: Find the area enclosed between the x-axis and the curve y = (x+ 3)²,0 < x < 1.

A:

Q: Find the area bounded by the given curves. y = x2 − 5 and y = 4 − 8x2 _____________ square units

A: Given curves y=x2-5 and y=4-8x2. The objective is to find the area bounded by the curves.

Q: Compute the area bounded by the curve y = x² – 2x , the x-axis and the ordinates x = 1; = 3.

A: We have to find the area bounded by curves

Q: find the area bounded by the curve y=9-x^2 and the x-axis

A:

Q: Sketch the graph and find the area bounded by the curves for y = 2x² and y = x² + 4

A: Given query is to find the area bounded by the curves.

Q: Find the area bounded by the given curves. y = 8x' + 3 and y = 8x + 3 square units

A:

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

A:

Q: Find the area bounded by the parabola y2= 4x, the x – axis and the lines x=1 and x=3.

A:

Q: Determine the area bounded by the curves Y = -x² – 18x + 88 and y = (x – 4)².

A: To determine the area bounded by the curves

Q: . Find the area between the curves y =x+1 and y=2x+1

A:

Q: find the area baunded by the curves linest ytAx-8 =0 and y=x

A:

Q: Find the area between the curves: y = x3 – 12x? + 20x and y = -a3 + 12x2 – 20x

A: Solution )

Q: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

A:

Q: . Calculate the area bounded by the curve y= 4(x – 1) and the x -axis. A)

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.