For F(x)= 3+3x-2x^2 A. Sketch the graph and the rectangles from x=0 to x=2 using n=4 and right endpoints. b. Estimate the area under the graph

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

A:

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

A:

Q: Estimate the area under the graph of f(x) = x² + 3x +1 over the interval [3, 5] using five…

A:

Q: Estimate the area under the graph of f(x) = 4 over the interval [2, 5] using five approxima %3D…

A: Given: f(x)=4x

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [-1, 2] by…

A: Clearly the given integral can be approximated by the areas of the given triangles.

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

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

A: Given function :

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

A:

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

A:

Q: The sum that best approximates the area under the curve between the function and x-axis on the…

A: our objective is to find the best approximation

Q: Approximate the area under the graph of ƒ(x) = 2x + 3 and above the x-axis from x = 0 to x = 4 using…

A:

Q: Estimate the area under the graph of f(x)=x^2+4x from x=1 to x=5 using 4 approximating rectangles…

A: The given graph of the function is f (x) = x^2+4x from x = 1 to x = 5.The number of triangles is…

Q: Estimate the area between the graph of F(x) = 10x2 - 7 from x = 1 to x = 7 using three rectangles…

A: We have to find the area using left end sum .

Q: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

A:

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9- x over the interval -2, 1] by using…

A: To find:- Estimate area between the x Axis and graph of f(x) = 9-x2 ove  interval [-2, 1] using…

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 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: Estimate the area under the graph of f(x) = x² + 2x + 1 over the interval 1, 6 using four…

A:

Q: Using left endpoints, approximate the area under the curve of f(x) =3x^(2) + 1 over the interval [0,…

A:

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

A:

Q: the area between the curves x^(2) and x^(4)

A:

Q: Estimate the area under the graph of f(x)=5/x from x=1 to x=7. Approximate using 6 rectangles.A.) If…

A: There are 6 rectangles  So each rectangle is of width = (7-1)/6=6/6=1 So, endpoints are…

Q: What is the area under the curve for f(x) = 3x2 +5 between x=1 and x=10?

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: The area between the curve y = = and the x-axis from x = 10 to x = 20 is the same as the area…

A:

Q: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

A:

Q: Estimate the area under the graph of f(x)=x^2+2x from x=5 to x=11 using 3 approximating rectangles…

A: Given: f(x)=x^2+2x and 5 ≤ x ≤ 11

Q: Estimate the area under the graph of f(x)=5 root x from x=0 to x=4 using four approximating…

A: a = 0; b = 4; n = 4; Width = Δx = (b - a) / n = (4 - 0) / 4 = 1

Q: Find the area between y=ln(x-6) and y = (ln(x-6))2

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: What is the area of the region below the graph of the square root function and above the x-axis from…

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 between the curves x2 and 6x – 5

A:

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

A:

Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

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

A:

Q: You can use a calculator to help you but please show me each step with what you calculated. Estimate…

A:

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

A:

Q: Estimate using right-hand endpoints, the area between the curves y=9x^2 +30 and y= 5-7x over the…

A: given :

Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 4 using right sum with two…

A:

Q: About the right and left approximations of the area between a curve and the x-axis, it is correct to…

A: Right approximation: while finding approximate area by the sum of small rectangles, if we make the…

Q: find the area between y=2x2+9x-5 and y=-X2+6x+1 for x in (-2,2)

A: The given curves are,

Q: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

A: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

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: Estimate

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.