An area is enclosed by the curve y = 2x + x^2 - x^3 and the x - axis. Find %3D the area below the x-axis. *

Q: Find the area below the x-axis and bounded by the curve  y=1-2x for 5<=x<=7.

A: The given curve is: y = 1 - 2x;  where 5 &lt;= x &lt;= 7 The graph is as follows:

Q: (a) Estimate the area under the graph of f(x) = 2+ 4x² from x = -1 to x = 2 using three rectangles…

A:

Q: Iwo curves having an equation of x = 2Vy and Compute the area between the two curves.

A: Given,          x=2y    and    y=2x

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

A: Given function :

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

A:

Q: 4. Find the area bounded by the curves y = 2x – x2 and the x-axis

A:

Q: -2 V2x - x² dx

A: The given integral,       ∫022x-x2 dx

Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: ) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the…

A: Area under the curve =∫ab(upper curve -lower curve)dx

Q: Determine the area enclosed by the curve y=5x2+2, thex-axis and the ordinates x=0 and x=3. Find also…

A:

Q: Find the area between two curves: 1. Determine the area below f(x) = 8x - 2x2 and above the x-axis.

A: Given: curve y=8x-2x2To Find: Area between the curve and above the x-axis

Q: 7. y=- y=0, x =1, x = -1

A: We will solve for first part only. Given equations of curve: y2-6y=-xy2-2y=x

Q: g(x) = 2x2 - x - 1, [3, 5], 4 rectangles < Area <

A: To use the right endpoint and left endpoint Riemann integral to approximate the area by the given…

Q: Find the area bounded by the graphs of the indicated equation y = x2 - 5; y= 4; 0sxs3 The area is…

A:

Q: The area bounded by the x-axis and the parabola y = 6 - x - x?

A: The solution is given as

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 area between the curves. x= - 2, x = 2, y =7x, y=x² - 8 The area between the curves is

A: Given,           x = -2,  x = 2,  y = 7x  and  y = x2 - 8

Q: The area bounded by the curve y2=12x and the line x=3 is revolved about the line x=3. What is the…

A: The correct answer is option C. Given  y2=12x and equation of line x=3 The point at which the line…

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 f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

A:

Q: Sketch the graph of y = 2x on the interval [0, 3]. Shade the area between the curve and the x-axis.…

A: We have to sketch the graph of y=2x on [0,3] And find the shaded area

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

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

A: The objective is to find the total area.

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9.

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.

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 TOTAL geometric area bounded by the curve given by f(x) = x ^ 5 - x ^ 3 and the r-axis on…

A: Given function is : fx=x5-x3

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

A: Given data: The first equation given is x=-5. The second equation given is x=3. The third equation…

Q: Find the exact area of the region bounded by the x-axis and the graph of y = x - x. Area =

A: Solve for area

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

A:

Q: Find the area under the graph of y = 4x + 3, above the x-axis, between x = 1 and x = 4. (You can use…

A:

Q: find the area of the region enclosed by the curve defined by y=x^(2) -2x-15 and the x-axis. Please…

A:

Q: The total area bounded by the graph of y = 5 - x, the line a x = 0 and the x-axis

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

A:

Q: Find the area between the curves.    x = - 5, x = 1, y = 10 x, y= x 2 -11

A:

Q: Use a graphing calculator to find where the curves intersect and to find the area between the…

A: To Determine: Use a graphing calculator to find where the curves intersect and to find the area…

Q: There is a line through the origin that divides the region bounded by the parabola y=6x−2x^2 and the…

A: y = 6x - 2x2 y = 2x ( 3 - x )  Hence, this parabola crosses x axis at x = 0 and x = 3

Q: What is the area of the region bounded by the graph of the function below? 2x + y = 8, x-axis and…

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 of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

A:

Q: Find the area the region lying between the x axis and the curve y=(ln(8x)-1)/x2 to the right of the…

A: Given curve is y=ln(8x)-1x2 Since region lying between x-axis and the curve to the right of the line…

Q: Find the area of the region above the curve y = x2-6, below y= x, and above y=−x.

A:

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

A: The Left Riemann Sum (also Left Endpoint Approximation) uses the left endpoints of a subinterval.

Q: Determine the area enclosed by the curves y =-x + 4x and y =-x+4. Draw a sketch of the graphs on the…

A: The shaded region represents the region enclosed by the given two curves.

Q: Find the area between the graph of y = x² – 2 and the x-axis, between x 0 and x = 4. %3D

A: Use integration to find the area.

Q: Estimate the area of the region under the curve        y = -x3 + 5 and above the x-axis for…

A:

Q: Find the net area and the area of the region bounded by the function y=5-|x| and the x-axis between…

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.