Use a finite approximation to estimate the area between the x-axis and the graph of f(x)=2x^5 between x=0 and x=1.

Q: Estimate the area under the graph of f(x) = 9 – x° over the interval [ – 2, 1] using ten…

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Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Determine the area bounded by the curves y=sinhx, y=coshx, the y-axis and the line y=1.

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Q: stimate the area under the curve  -(x)2+

A: Here we have to find the area under the curve -x2+1 with an interval of 0,14.

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

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Q: . Find the area bounded by the curve f(x) = (2+x)(x – 5), the lines = -2, line = 0 and the x - axis.

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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 under the graph of f(x)=√x+2 over the interval [ - 2, 0] using eight approximating…

A: To estimate the area under the graph of fx=x+2 over the interval -2, 0 by using eight approximating…

Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

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

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Q: Estimate the area under the graph of f(x) = 16 - r² over the interval [- 4, 1] using ten…

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Q: Estimate the area under the graph of f(x)=1/x from x=1 to x=2 using left and right endpoints.

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Q: What is the area bounded by the curve x² = -9y and the line y + 1 = 0?

A: Given curve is x2=-9y Line is y+1=0 We need to find the area bounded by the curve

Q: Estimate the area under the graph of f(x)=x^2+4x from x=4 to x=7 using 3 approximating rectangles…

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Q: The graphs of y = 1 − x2 and y = x4 − 2x2 + 1 intersect at three points. However, the area between…

A: Given curves  y=1-x2 y=x4-2 x2+1 Graph :

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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Q: Estimate the area under f(x)-cos x on[ Approximation with 3 rectangles under the curve. (On such a…

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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: Please estimate the area under the curve c(x)=1−x3 for 0≤x≤1 using 4 rectangles with width 1/4.

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Q: Find the area bounded by x2- 6x +y = 0, x² - 2x - y = 0. and the x-axis.

A: We have given two curves;

Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

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

A: Area

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

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Q: What is the area bounded by the curve y = x3 and x = -2 and x = 1? What is the area bounded by the…

A: we have to find area

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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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   between x=0 and x-4

Q: Find the area between the curve y = 9 − (x/2)^2 and the line y = 6 − x.

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Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

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

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Q: find the area bounded by the curve y=9-x^2 and the x-axis

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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: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

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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: Estimate the area under the curve of f (x) = = from 1 <x< 2 by using four sub-intervals and…

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Q: Estimate the area under the graph of f(x) over the interval [– 1, 2] using five approximating x² + 3…

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Q: Estimate the area under the curve from x=0 to x=5 using 5 approximating rectangles and left endpoir…

A: In this question, the concept of Riemann Sum is applied. Riemann Sum To estimate ∫abfxdx, Riemann…

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  show full solution

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Q: What is the area bounded by the curve y = x3, the x-axis, and lines x= - 2 and x = 1?

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Q: By integration, determine the area bounded by the curves y = 6x – x2 and y = x2 – 2x.

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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: 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: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  Show full complete solution.

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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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: Use the Midpoint Rule to estimate the integral. n=4

A: Since we have been given up the integral ∫191xdxOur aim is to estimate the integral till n=4 using…

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.