pproximate the area under the curve y S(a) graphed below from a0 to z 6 with 4 sub-intervals using left endpoints L, midpoints Ma, and right endpoints R4 8- Round your awers to one dectmal (a) Preview (b) M. Peview () R Preview

Q: Find the area of the region between the curves y = x^3, y = -x, and y = 1. Round off to two decimal…

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Q: II. Find the area bounded by the curve y = x3 - 3x and the x-axis. Sketch the curve indicating the…

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Q: pproximate the area under the curve graphed below from x = 2 to x = 6 using a Left Endpoint…

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Q: Find the area of the region between the curves y 3x - 3 and y = - 2x² + 2 from x= - 1 to x= 1. The…

A: we draw the graph of given curve and find the required area . see 2nd and 3rd step.

Q: Use a graphing utility to find the intersection points of the curves, and then use the utility to…

A: y=5-x-22, y=ex Use the graphing calculator to draw the graph and mentioned the intersection point.

Q: nction f from a to b, and let L, and R, be the Let A be the area under the graph of an increasing…

A: In order to find n, the first step is to calculate the area under the curve y=ex from x=1to x=4. The…

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

A: Here, we need to estimate the area under the graph of f(x)=4x from x=0 to x=4 using four…

Q: pproximate the area under the curve over the specified interval by using the indicated number of…

A: our objective is to find the approximate area under the curve.

Q: Let R be a region bounded by x-axis, the curve y= cos.x between x= - 2 and x=-lines. If the region…

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Q: Q3/ Find the area of the region in the first quadrant that is bounded above by y = Vx and below by…

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Q: 2. Find the area of the region R enclosed by the curves given by the graphs of f(x) = v3x, g(x): =…

A: Area between curves

Q: Find the area of the region enclosed by y = 3.5x and a = 8.5 - y". |3D I 2 3. 7 Use horizontal…

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Q: ind the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A: y=2x-tan (0.3x), x=1, x=4, y=0 Area of the region is  A=∫14(2x-tan(0.3x))dx  = x214 -∫14tan(0.3x)dx…

Q: 0. Approximate the area under the curve y =Vx from x-0 to x=2 using R5, right endpoints with five…

A: To compute the area of the integral using right endpoints from 0 to 2.

Q: II. Find the area bounded by the curve y = x3 - 12 x and the x-axis. Sketch the curve indicating the…

A: Given curve is y=x3-12x

Q: How do you approximate the area under the graph of f(x) and above the x-axis using the following…

A: As per norms, the first three subparts a, b and c are answered. To find the approximate area under…

Q: (a) Estimate the area under the graph of f(x) = 2/x from x = 0 to x = 4 using four approximating…

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Q: V. Find the area bounded by the given curves; 1 y=0, x=1, x = - 1. y= 1+x² Sketch the curve…

A: Given, y= 1/1+x² y= 0 x=1 x=-1

Q: pproximate the area under the curve f(x)=x^2+ 1 from x = 2 to x = 5 using a Left Endpoint…

A: left end point sum

Q: c. Find the area of the reqion bounded by y xe-a and the x-axis on the interval 0,bl. Because this…

A: Given curve is The area of the region bound by the curve and x-axis on the interval [0,b] is given…

Q: ind the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A: The above given equations are: y=x2+3xx=1x=2y=0 The graph for these equations are:

Q: (a) Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = T/2 using four…

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Q: (b) Find the area between the graphs of f(x) = x and f(r) = z between I = 0 and r = 1. (Graph the…

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Q: (a) Estimate the area under the graph of fx) = 3/x from x = 1 to x = 2 using four approximating…

A: Given : f(x) = 3/x  Interval is from 1 to 2  So,  Step(h) or ∆x =(b-a)/n  for intervals a to b

Q: Find the area, A, between the curves y = In x and y = In 3x from x= 1 to x-2. The area is A = (Type…

A: We have to find the area between the given curves.

Q: Estimate Area under Curve: 1. a) Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2…

A: The function is fx=1x from x=1 to x=2. Here, for four rectangles n = 4 so the width of these…

Q: An area is enclosed by the curve y = 2x + x^2 - x^3 and the x-axis. Find the area above the x-axis.…

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Q: Consider the region bounded by the graphs of x-B =0 and x = y -D a. Solve for the points of…

A: Given: Region is bounded by x-B=0 and x=y2-Dwhere, B=5 and D=2 To Find: a. Solve for the points of…

Q: Consider the region bounded by x2 = y2 , x = 8 - y2, and the x-axis. a. Sketch this region. b. Find…

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Q: Find the area of the region R bounded by the graphs of the functions. f(x)= x , g(x) 1 h(х) — 2.…

A: The graph is drawn using DESMOS graphing calculator.

Q: QI] Find the area bounded by the following curves: A] y 5-x2 and y 2+ 4. BJ y = -Vx, y -x+3 and y 0

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Q: (5) the tangout to y = √9+2x of Latex x = 4 passes through the orign a) Find a 67 for this value of…

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Q: Find the area of the region R enclosed by the curves given by the graphs of f(x) = v3x, g(x) = -4x +…

A: To find the double integration first integrate x then y, for that draw a line parallel to x axis…

Q: Find the area between the curve and the x-axis over the indicated interval. y = [1, 6] The area…

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Q: 2) Zy? + X :0 + x -1 :0

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Q: In 2010 a particular factory produced computer hard drives at a rate of f(t) = 4.4e0.0175t thousand…

A: We are asked to find the area covered by the given functions: ft=4.4e0.0175t and gt=5.4e0.0164t for…

Q: II. Find the area bounded by the curve y = x3 - 4x and the x-axis. Sketch the curve indicating the…

A: Area bounded by a curve f(x) and x axis between the points x=a to x=b is, A=∫abf(x)dx

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

A: According to our policies we are allowed to solve one question at a time kindly repost other problem…

Q: Find the area of the region bounded by the curves y=x - 2x and y=x. (a)shade the region on the graph…

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Q: 2x + 2 Find the area of the region under the curve y = from a = 2 to b = 3. x – 1 Area =

A: We have to find area

Q: Q1 Sketch the graph of the curve y = (x – p)(x – p – 1)(x – p – 2) Shade the area of the region…

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Q: (a) Find all solutions to the equation x = 8 - x. %3D Show your work on Crowdmark, including your…

A: a)

Q: 1. Approximate the area under the curve y = x2 from x = 1 to x = 3 using a right sum with 4…

A: GIVEN: y = x2 from x = 1 to x = 3

Q: Let R be a region bounded by x- axis, the curve y= cosx between x= -lines. If the region Ris…

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Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A: We can find the area of the bounded by the given curves.

Q: e area of the region bounded by the positive x-axis, y-axis, the line x = 6 :

A: We have to find out the area of the region bounded by the given curves.

Q: Finda the area bounded by the given curves/lines. Sketch the graph of the curve and the plane…

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Q: An area is enclosed by the curve y 2x + x^2 - x^3 and the x-axis. Find the area above the x-axis. y…

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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.