Find the area of the region bounded by the graph of g(x) = (x − 4)^4 and the x-axis between x = 2 and x = 6.

Q: 4. Find the area of the region bounded by the graphs of y = x3 + 6x, x = 0, x = 2, and the x-axis.

A:

Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

A:

Q: Find the area of the region bounded by the graph of f(x) = x² + 1, the x-axis and the vertical lines…

A: Explanation of the answer is as follows

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 of the region bounded by the graph of y=x^2 -3x -4 and the -axis. y + 2 1 3 -1 -4 -5…

A:

Q: Find the area of the region bounded by the graphs of y2 = 4x and the line 2x - y = 12

A:

Q: The total area bounded by the graph of y = r- 1 and the x-axis is represented by 2.

A:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: y = 4Vx +. 1 y = 0, x = 1, and x = 9

A:

Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A:

Q: What is the area of the region bounded by the graph of the y= 2/x function x = e, x-e^2 lines and…

A:

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

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

A:

Q: Find the area of the region bounded by the graph of f(x) = 4 – x², the x-axis, and the vertical…

A: function f(x)=4-x2 To find area of region bounded by f(x), x-axis and the line x=1 and x=2.

Q: Find the area bounded by the graphs of y = 3x2; x = 0; x = 2; and the x axis.

A: Given,

Q: Find the area between the graph of y = 3x2 + x and the x-axis for x=0 to x=1. %3D

A: From the given curve the bounded region is shown below:     Now using the double integral method to…

Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

A:

Q: Find the area of the region bounded by the graphs of f(x) = 5 − x^2 and g(x) = x^2 − 3

A:

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A:

Q: Find the area between the graphs of y=8x-x+7 and y 3x -x+ 12

A: The given problem is to find the area between the given graphs. Given functions y=8x2-x+7 and…

Q: find the area of the region bounded by the graphs of f(x)=x2 and g(x)=8x

A:

Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

A:

Q: Calculate the exact area bounded by the x-axis and the graph of y=10−7x+x^2

A:

Q: Find the area of the region bounded by the graphs of the functions y=9-x² and y=x+3.

A:

Q: What is the area of the region between y = x - 2x- 3 and the x-axis from X = - 2 to X = 0?

A:

Q: Find the area of the region bounded by the graphs of y2=1-x and 2y= x+2.

A:

Q: Find the area of the region by bounded by the graphs of y=x2+2x and y=-x+4 on the interval [-4,2]

A:

Q: f (x) = x – 2x – 3

A:

Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

Q: Find the area of the region lying to the right of x = y2 - 5 and to theleft of x = 3 - y2.

A: Given: f(y)=y2-5 and g(y)=3-y2 To find: Where the curve intersect and it is calculated when…

Q: What is the area of the region between y=x^2-2x-3 and the x-axis from x-0 to x=6?

A: Given,      y= x2-2x-3and the x-axis  from  x=0 to x=6.

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A:

Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

A:

Q: 7. Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line p through the…

A:

Q: Example: Find the area of the region in the first quadrant that is bounded above by Y1 =Vx and below…

A: The graph is shown below:

Q: Find the total area bounded by the graph of y = x² + 2x and the x-axis on [-2, 2).

A:

Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. - -

A: Graphically: Now, the area can be found as the following.…

Q: Find the area of the region bounded by the graphs of y = x +6x, x = 0, x = 2, and the x-axis.

A: Answer

Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

A:

Q: How do I solve this problem?

A:

Q: Find the area of the region between the graphs of y = 13 – x² and y = over the interval 3 < x < 8. –…

A: Solve by integration

Q: Q1: The area of the region bounded by the graph of y=-0.5x+4and y=3x in first quarter.

A:

Q: The exact area of the region bounded by the graphs of y = x² + 2, and the x – axis from x = -1 to x…

A: Given graph of y=x2+2we need to find the area of the graph and the x-axis from x=-1 to x=2

Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

A:

Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

Q: Find the total area bounded by the graph of y = x² + 2x and the x-axis on [-2,2].

A:

Q: Find the area of the region bounded by y=-x^2+3x+1 and y=-x+1

A: Please see the diagram below to understand what's going on:

Q: What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-9?

A:

Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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.