Use a finite approximation to estimate the area between the x-axis and the graph of f(x)=25−x^2 between x=−5 and x=5.

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Estimate the area under the graph of f(x)=x^2+4x+9over the interval [0,7][0,7] using ten…

A: Given function :

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

A: See below

Q: y= -x² + 9; 0 sxs5 x< + 9; 0 < x< 5

A:

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 between the curves (x^2)-(y^2)=9 and the line y=2x-6

A: Recall: Area between two curves:          A=∫abf(x)-g(x) dx           OrA= ∫abUpper function-(Lower…

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)=√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: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

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

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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: Find the area under the curve y=2x6y=2x6 over the interval [0,3][

A: Solution

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

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Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

A:

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

A:

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: problem in photo attached

A: Given,

Q: find the total area of the region between the graphof ƒ and the x-axis. ƒ(x) = 1 - √x, 0 ≤ x ≤ 4

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

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

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Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. With graph

A:

Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

Q: Estimate the area under the graph of f(x)=x^2+2x from x=2 to x=10 using 4 approximating rectangles…

A:

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: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

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

A:

Q: Use left endpoints and 6 rectangles to find the approximation of the area of the region between the…

A: Let's find.

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

A: Explanation of the answer is as follows

Q: The area of the region bounded by x = /9-y', the y-axis and the line x-y in the first quadrant is:

A:

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

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

A:

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

A:

Q: What is the area of the region between y=x^2-2x-3 and the x-axis from x-0 to x=6?

A: Given,      y= x2-2x-3and the x-axis  from  x=0 to x=6.

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

A:

Q: Find the area of the region between the curves y = 8 - x2, y = x², x = -3, and x = 3. Area between…

A:

Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

A:

Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Given that, The curves are y=x2+5 and y=-x2, the line x=3, and the y-axis. Find the area bounded by…

Q: Estimate the area under the graph of ƒ(x) = 1/x​ from x = 1 to x = 2, first using 4 approximating…

A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

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

A:

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

A:

Q: Find the area of the region bounded by the graph of the function y = the x-axis, and the lines x = 4…

A: Definition used-                 The area under the curve of a function f(x) is given by -…

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

A:

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

A:

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

A:

Q: Estimate the area under the graph of f(x) = 49 – x² over the interval [ – 2, 6] using five…

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.