Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two vertical %3D lines x = 3 and z = 4. A = Preview

Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 4x, y = 0

A: We first find where the two equations meet.  We plug y=0 in the first equation and find x

Q: Find the area of the region bounded by the line y = 2x − 5 and the parabola y = x2 - 4x

A: The objective of the question is determine the area between given line and parabola.

Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x-axis and the parabola x² +…

A: Graph:

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y² –…

A:

Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 10x, y = 0

A:

Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: Find the area bounded by the parabola x = 8+2y-y², the y-axis, and the lines y = -1 and y = 3.

A:

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

A: Given equation y=-x2+6x,  y=0. The objective is to find the area of the region. "Since you have…

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 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: y2 = 4 – x and y² + y = x + 2

A:

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

A:

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 of the region between the line y=2x and the curve %3D y =x² +x-2.

A: Given:          y=2x and the curve y=x2+x−2

Q: Find the area of the region bounded by the graphs of the equations y = 1+ Vx y = 0,x = 0, and x = 8

A: Solved below

Q: Find the area of the region bounded by y = xInx and the x-axis between x=1 and x = e

A: Using formula of Area Under The Curve.

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: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

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 region bounded by the parabola y^2=x+3 and the line x - y = -1

A:

Q: Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum…

A: To find the are bounded by the curves and lines: (a) y=xe-x, the x-axis and the maximum ordinate.

Q: Find the area of the region bounded by y=2x2-3x+2 the x axis and the vertical lines x=0 and x=2

A:

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 bounded by y² = 4a(y-x), y² = 2a(x+2y-3a) and the x-axis

A:

Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

A:

Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 8x, y = 0

A: Let us plot the region.

Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

Q: find the area of the region bounded by the parabola x=y^2+2 and the line y=x-8

A:

Q: Solve the area bounded by the curve x=y^2 and the line y=x+1, y=2, and y=-2. Graph manually.

A:

Q: Find the area of the region bounded by y = x² - 5x + 6, the x axis, and the vertical lines x = 0 and…

A: Given that y = x2 - 5x + 6 ; y = 0 (x - axis) ; x = 0; x= 4  We have to find the area of the region…

Q: Find the area of the region bounded by the curves, y = -6, y = 6,the y – axis and the parabola y² –…

A:

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

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: Find the area of the region bounded by y=2x2 -3x+2 the x axis and the vertical lines x=0 and x=2

A: Given that a equation y(x) and we find area bounded by x=0 ,  x= 2  . Here i attached solution of…

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 between the curve y = 2x² + 4x-6 and the x-axis from x = -2 to x= 3. %3D %3D %3D

A:

Q: Find the area of the region between the x-axis and the curve .3 y = x³- 4x - 2 < x<2 ?

A: Let us first plot the graph of y=x3-4x, -2≤x≤2.

Q: 2 - 41 -y =0 /2

A: Area of curve = integration of ydx from x1 to x2

Q: find the area bounded by y = (2x - 3) / (x^2 + 4), the coordinate axes and the minimum ordinate

A:

Q: Find the area R- region in the first quadrant that lies below the curve y=x^2+4 and is bounded by…

A: The given problem is to find the area of region R bounded below by the given curve and the line.…

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y2 -…

A:

Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2…

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.