Find the total area bounded by the x-axis and the curve y=f(x) on the indicated interval. Enter your answer in exact form or as a decimal number rounded to the nearest thousandth. f(x)=4(2x+3)^2;[4,6]

Q: Find the area of the region between the graph of y=x+2, above x-axis, and between the lines x= -1…

A: Given:

Q: Find the exact area between f(x) = 2x and g(x) = 15 – x from the vertical axis to their point of…

A:

Q: How many individual areas in the total area bounded by the curve y=x - 3x +2x and by the x-axis from…

A: first we plot the given region then decide how many areas exist

Q: y= -x² + 9; 0 sxs5 x< + 9; 0 < x< 5

A:

Q: Compute the area bounded by the curve y = 3x - x2, the x-axis and the ordinates x = 2; x = 4.

A: We need to evaluate the area bounded by the following curve : C1 : y = 3x-x2 C2 : x -axis C3  : x =…

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

A:

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

A:

Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: Find the area bounded by the curve y = 62xe-62x and the x axis from x =0 to x = 4

A: Area bounded by the curve y=f(x) and x-axis from x=a to b is given as, ∫abf(x)dx Some common…

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.

A: so we have and the other function is

Q: Find the area between the curves x² and 3x – 2

A:

Q: Find the area of the region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and…

A: The region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and x = 2 is as…

Q: What is the area under the curve of the following positive function y = 10x4 + 3x² between x = -1…

A:

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

A:

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A:

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct 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: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

A:

Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

A:

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

A:

Q: Find the exact area under the curve between the indicated values of x. y = -x2 + 9; between x = 0…

A:

Q: Find the area included between x2+ y2= 4x and y2= x above x-axis

A: Find the area included between x2+ y2= 4x and y2= x above x-axis

Q: Find the total area between y = -x2 - 2x and the x-axis for -3 sxS2.

A: The objective is to find the total area.

Q: The area under the curve y = 2x bounded from below bythe x-axis and on the right by x = 4 is 16 3…

A: Given that the area under the curve y=2xwe need find the area below the x-axis and the right by x=4

Q: Find the area bounded by the loop of the curve y² = 4x²-x*

A: The given equation of the curve is: This can also be written as: The graph of this curve is:

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

A:

Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

A:

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

A:

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

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

A:

Q: Find the area between the curves x=63-7y^2 and x=7y^2-63

A: Here two curves are given and we need to find the area between them. The curve equations are shown…

Q: Find area of the region under the curve y = 5x - 4 and above the x-axis, for 3 < x < 5.

A:

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

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

A:

Q: Find the area between the curves x2 and 6x – 5

A:

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

A:

Q: Find the area of the region bounded by f (x) = a 20 – 3x – 2x2 and the x -axis using Simpson's Rule…

A:

Q: Find the total area under the curve f(x) = 2xer² from a 2xe from x = 0 and a

A:

Q: Find the area between the curve and the x axis over the indicated interval. Y=4-x square; [-2,2|

A: Given: Y=4-x2 to find out: area between the curve and the x -axis over the interval [-2,2]

Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

A:

Q: Find the total area between the curve of the function f(x)=−2x and the x-axis over the interval…

A:

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

A: Given f(x)=x2+x-20. Find the area bounded by x-axis and f(x) on [2,5].

Q: - Find the total area between y = x/3- x and the x-axis for -1 sx< 8. %3D

A:

Q: Compute the area bounded by the curve y = x2 + 3, the x-axis and the ordinates x = 1; = 4.

A:

Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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.