3) Find the area of the region bounded by the graph of f(x) = (x - 5)2and the x-axis between x %3D =0 and x = 5. %3D %3D

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

A:

Q: (13) Find the area of the region between the line y = 2x and the curve y =x² +x-2 %3D

A: The given two curves are y = 2x y = x2 + x - 2

Q: 18.Find the area bounded by the graph y = 30x – 3x² and the x – axis. %3D

A:

Q: Find the area of the region between the graphs of y = 16 – x² and y = - 3x – 24 over the interval –…

A: The objective is to find the area.

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

A:

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: What is the area of the region between the graphs of y = x – 1 and y : -X – 1

A:

Q: 1. Find the volume of the solid formed by revolving the region bounded by the graph of f (x) = -x² +…

A: Given problem:- Find the volume of the solid formed by revolving the region bounded by the graph of…

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

A:

Q: 16. Find the area of the region bounded by the graphs of the equations, y = -x² +x+ 6, y = 0

A:

Q: Suppose you want to approximate the area of the region boundedby the graph of ƒ(x) = cos x and the…

A:

Q: 1. Find the area of the region bounded by the graph of the equation r = 3 cose. %3D

A: Concept Used: Area in polar coordinates is given by Area=12∫abr2dθ

Q: 7. Find the area of the region bounded by the graph of y= 2x² – 3x+2, the x-axis, and the vertical…

A: The equation of the curves are: C1: y = 2x2-3x+2C2: y = 0C3: x = 0C4: x = 2 To evaluate: The area…

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: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: Find the area of the region under the graph of f (x) = 4 − x2 over [0, 2].

A:

Q: 13. Find the area of the region bounded by the graphs of y = x, y = -x + 8, and y = 0

A:

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

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

A:

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: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x2.

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: 7 Find the area of the region bounded by the a graphs of f(x) = x+ 2x+1 and gix) = 3x+3. Write…

A: The given curves are: f(x)=x2+2x+1          and          g(x)=3x+3

Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

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

A:

Q: 1. Find the area of the region bounded by y^2=8x and y=x

A: Region bounded by these two curves will be given as

Q: 3. Find the area of the region bounded by x = 3 – y² and the line y = x – 1. Sketch the graph of the…

A:

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

A:

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

A:

Q: Sketch the graph of the curve y (x-p)(x-p-1)(x-p-2) Shade the area of the region bounded by the…

A:

Q: 4. Find the area of the region bounded by the curves x-y² = 0 and x+2y² = 6.

A: Hence, the area of the region bounded by the curves x-y2=0 and x+2y2=6 is 82 square units .

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

A: Given curve y=x3-x2-2x. The objective is to determine the area of the region bounded by the curve…

Q: 18) Find the area of the region bounded by the graphs of y = x + 2 and y = x².

A:

Q: 1. Find the area of the region bounded by the curves y = |x² - 4| and the curve y =x2 + 4 %3D

A: One of the two main parts of calculus is concerned with the study of integrals, as opposed to…

Q: 1. Find the area of the region bounded by the graphs of y = x² + 2, y = -x, x = 0, and x = 1. Hint:…

A:

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

A:

Q: of the given equations. y = x² - 2x - 24, y = -x² 1

A: Given curves are      y=-x2             . . . (1)    y=x2-2x-24  . . . (2) The graph is given be

Q: 6. Find the area of the region bounded by the graphs of f(x) = 2 - x and g(x) =x.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: 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: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

A:

Q: 3. Find the area bounded by the curve y = - x² x = 1, and the x-axis. %3D x4 – 16

A: We first sketch the region using a graphing calculator.

Q: 17) Find the area of the region bounded by the graphs of y = 3x² and y = 12.- %3D

A:

Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region bounded by x=y2-4 and x=3y. The rule for integration…

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

A:

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

A: Given that:

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

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.