Let f(x)=-2x^ 3 +6x^ 2 -x+1, Use L 4 to estimate the area under the curve or the interval [- 1, 1] ). Your work must include a careful sketch of the graph and the rectangles you're using

Q: What is the total area between f(x)=6x+6 and the x-axis over the interval [−6,3]?

A: To calculate the total area bounded between the curve f(x)=6x+6 and x-axis over the interval [-6,3].…

Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. + dx -2

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Q: Use finite approximations to estimate the area under the graph of the function f (X) = x³ between x…

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

Q: Estimate the area under the graph of f(x)=1/x+3 over the interval [-1,2] using ten approximating…

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Q: Use finite approximations to estimate the area under the graph of the function f(x) = x² + 1 between…

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Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A: Given curve: fx=x2+1 We have to find area under the given curve from x=0 to x=2. It is given that we…

Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

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Q: Estimate the area under the graph of f(x) = x° between x = 0 and x = 4 using each finite…

A: Given,  f(x)=x3 and a=0 and b=4

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

A: We need to divide [1,2] in 4 equal intervals. Width of each interval=(2-1)/4=0.25 So the partition…

Q: What is the total area between f(x)=2x−7 and the x-axis over the interval [0,5]?

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

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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: Use finite approximations to estimate the area under the graph of the function f(x)=3−x2−2x between…

A: The Given function is, f(x)=3-x2-2x  Between x=-3 and x=1 Here we have to find the area under the…

Q: Sketch the graph the integrands and use areas to evaluate the integrals. V16 – x² dx

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Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

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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: Estimate the area under the graph of f(x) = 2x between x= 0 and x = 8 using each finite…

A: Width of the interval [0,8] is (8-0)=8For two subintervals , width of each interval=82=4So the…

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

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

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

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Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 2 using left sum with two…

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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: Use the Midpoint Rule to evaluate the integral Sx-dx.

A: Midpoint rule:Let f(x) is a polynomial of degree ⩽n-1Let the midpoint x1=a+b2 and…

Q: The area of the region bounded by the graphs of y = x3 and y = x cannot be found by the single…

A: Given: y=x3, y=x for finding area of region bounded by given curves, first we draw graph of each…

Q: Estimate the area under the graph of f(x) = x° between x = 0 and x= 4 using each finite…

A: Given: f(x)=x3   between x=0 and x-4

Q: Find the area of the region bounded by f(x) = -x² – 2x + 3, x-axis, and interval [0, 2].

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Q: Estimate the area under the graph f(x)=1/(x+3) Over the interval (-2,1) Using 8 approximating…

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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: Use a finite sum to estimate the area under the curve using the midpoint rule f(x)=x^3 on the…

A: Width of the interval [0,2] is = 2-0=2So for two rectangles the width of the subintervals=∆x=22=1So…

Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval (0, 7 using ten…

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Q: Estimate the area under the graph of f(x)=x+4 over the interval [-4,4] using eight approximating…

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Q: 1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point…

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Q: Estimate the area under the graph of f(x) : 1 over the interval [- 1, 1] using ten approximating…

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Q: Find the area of the region bounded by the graph of f(x) = x(x + 2)(x - 1) and the x-axis on the…

A: Area of the region bounded by f(x) and x- axis

Q: To estimate the area under the graph on the interval [-4, 4], we use left-rectangle approximation…

A: Introduction: A sub-interval can be divided into a certain number of subintervals with equal length.…

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: Find the total area under the curve f(x) = 2xer² from a 2xe from x = 0 and a

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

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

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Q: Approximate the area under the curve 4=メ Right Endpoint from x=3 to メニの USing approximation with 6…

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Q: Estimate the area under the graph of f(x)=36−x2f(x)=36-x2 over the interval [−5,2] using five…

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Q: Estimate the area under the curve  y=(x+5)2-2 on the interval from x=0 to x=4.

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Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg.

A: To find area under a curve y=f(x). Integrate f(x) from x = a to x = b.

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 the area under the graph of f(x) = 16 – x² over the interval [– 1, 4] using ten…

A: RIGHT HAND SUM Consider the following variable, n=number of rectangles∆x=width of each…

Q: Estimate

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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.