calculate the area of the bounded figure from the graph of the function y = x²-1 and the axis Ox

Q: Find the area of the region bounded by the graph of the function f (x) = x, the X−axis, and the…

A:

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

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

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: Sketch the region bounded by the graphs of the equations f(x) = − 4/x3,         y = 0, x = −3, x =…

A: The graphical representation of the region bounded by the above equations is,

Q: Find the area bounded by the parabola y^2=4x and the line 2x-4. (with graph)

A:

Q: Find the area of the region bounded by the curves.  y = x(x2 - 1) and the x-axis

A: Given curves are, y=x(x2-1)and the x-axis y=0 .   First, find the intersection points:…

Q: Find the area of ​​the region bounded by the y=x3 and y=2x-x2 curves.

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: Sketch the region bounded by the graphs of the equations f(x) = x2 + 2x, g(x) = x + 2 and find the…

A: The region bounded by the graph is as below

Q: Find the area of the region bounded by the graph of y = x /(x2 + 1) the x-axis, and the line x = 3

A:

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 bounded between the curves 5x-y x2 and y = 3x + x²

A: We have the given the curves y=5x-x2 and y=3x+x2 We have to find the area bounded by this two given…

Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

A:

Q: the area bounded by the curves y=2-x2 and y=x2 is

A:

Q: Calculate  The  area bounded by the function  f(x)=x3-4x+3, as lines x = 0, 2 ,x=2 and the x-axis

A:

Q: Find the area of the region bounded by the curves y = x ^ 3 - 12x, y = x ^ 2.

A: y = x ^ 3 - 12x, y = x ^ 2.

Q: Find the area bounded by the ff. curves and lines: a. x^2 - y^2= 9 and y= 2x - 6

A: x2-y2=9  &  y=2x-6 The diagrammatic representation of the area is,

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

A:

Q: y = 4/x, y- 4y + 2x = 5 and the line y = 4

A: Sketch the region and integrate in y variable.

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: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Determine the area bounded by the curves y = -x² – 16x + 36 and y = (x – 2)².

A: Answer

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 of region bounded by the curve y=x²-2x and y=-x²+4

A:

Q: Find the area bounded by the curve x=y²+2y and the line x=8.

A:

Q: Find the area of the reglon bounded by the graphs of the equations. y = 5x +5, x = 0, x = 2, y = 0

A: Required area is…

Q: Sketch the region bounded by the graphs of the equations f(x) = 3√x − 1,   g(x) = x − 1 and find the…

A:

Q: Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) = 6Vx…

A: Given function is - f(x)=6x We need to find area of the region  under the graph of f(x) on interval…

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

A:

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

A:

Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,

Q: Sketch the region bounded by the graphs of the functions. y = x2 - 4x + 4, y = x2 - 12x + 36, y = 0

A:

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

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

A:

Q: Find the area of the finite region bounded by the curve y = 12 + x - x2 and the line: y = x + 3.

A:

Q: Find the area of the region that is completely bounded by the two curves f(x) = x* g(x) = 3x + 20. -…

A:

Q: Find the area of the region bounded by the curve  y = 2x2 - x  and the line  y = x + 4  .

A: To find the area of the curve.

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

A:

Q: Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) = 5Vx…

A: The function is given by fx = 5x To evaluate : The area of the region under the graph of the…

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

A:

Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: y = 2x ,2 y+ 4x – 8 = 0

A:

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

A:

Q: %3D y = x²– 2x

A: Here we have to find the area bounded by the curves y=6x-x2 ............... (1) and y=x2-2x…

Q: Determine the area bounded by the curve y = x2 - 3x -6 and lines y =-4-x,x = 0 and x = -2.

A:

Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

A:

Q: Estimate the area under the graph of f(x)=√x+3 over the interval [−3,1] using eight approximating…

A: Given :  Function f(x) = √(x+3), Interval [-3,1], To find : Area under the graph of given function…

Q: Find the area bounded by the curves y=x4-2x2 and y=-x2+4 at an [-1, 1].

A: The region bounded by the curves y=x4-2x2, y=-x2+4 in [-1,1] is:

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.