Approximate the area under the graph of​ f(x) and above the​ x-axis with​ rectangles, using the following methods with n=4 f(x)= 2/x+5 from x=1 to x=9 a) use left endpoints b)use right endpoints c) average the answer in part a and b d)use midpoints

Q: Find the area enclosed by the curves f(x) = 16x and g(x) =2x4

A: We need to find the area enclosed by the curves

Q: (A) Estimate the area under the graph of f(x) = 16 – 2? from x = 0 to x = 4 using 4 approximating…

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Q: Calculate the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=8x+80 and bounded below…

A: The solution of the problem is given in the next steps.

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

A: Given function is fx = sinx x∈0,  π2 number of rectangles = 4 Step size  h= π2 -04   = π8 ⇒ h = π8…

Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles…

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: (a) Estimate the area under the graph of f(x) = 25 – x from x = 0 to x = 5 using five approximating…

A: Consider the equation as shown below: Here, the function fx =25-x2 And the object is to find the…

Q: find the area bounded by the following curves and lines  y = 3x/square root of x+4  where y = 0 and…

A: The given region are: y=3xx+4, y=0, x=4

Q: 6. Calculate the area enclosed between y=x-4x2 – 5x and the x-axis.

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Q: What is the area enclosed between the graphs of X 4 and x = y² – 5?

A: Area between two curve

Q: Find the area enclosed by the curves f(x)=39-x2 and g(x)=x2

A: Given curves

Q: Estimate the area under f(x)=x^3 from x=1 to x=5 using n=4 rectangles and choosing heights via: (a)…

A:

Q: 2. Approximate the area under the graph of f(x)= 25–x² from x=0 to x= 5 using the midpoints of five…

A: Area of graph under f(x) = ∫05f(x)dx

Q: Find the area between the corves y= 2-x² and

A: Find the area between the two given curves First draw both the equations in a single plane To draw…

Q: Find the area under the parabola y = 8 - x^2 -2x, above the x axis

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Q: Find the area bounded by f(x) = 4x − x2 and the x-axis. (In square units)

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Estimate the area under the graph (sqr-root):x+4 over the interval [-4,12] using 8 approxiamating…

A: Given function: Width of each interval = (12-(-4))/8= 16/8= 2  So the partition is -4, -2, 0, 2, 4,…

Q: Let f(x)=-2x^ 3 +6x^ 2 -x+1, Use L 4 to estimate the area under the curve or the interval [- 1, 1]…

A: L4 is the left endpoint of the expression with 4 approximating rectangles.

Q: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

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Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: Find the area bounded by the curve of y = x' + 3 and the x-axis from x = -3 to x = 1 Approximate are…

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Q: Find the area between the curve y = tan x and the x-axis from x = -pai/4 to x = pai/3.

A: Given information

Q: Find the area bounded by y^3 = x^3 + x^4 and the x-axis. Sketch this and label the important…

A:

Q: Estimate the area under the graph in the figure by using(a) the Trapezoidal Rule, (b) the Midpoint…

A: Given

Q: Determine the area bounded by the graphs of the following equations. y=coshx  , y=3

A: Given that, y = coshx  and   y = 3 we have to calculate the area bounded by both equation, Solve…

Q: What is the area enclosed between the graphs of X1 = y“ and X2 –3y + 4?

A:

Q: Use the Trapezoid Rule to approximate the area under the curve f(x) = 2x° + 1x – 3 from x = x = 11.…

A: Use trapezoidal rules

Q: Using the fundamental theorem, find the area under the curve y = 4x3 −2x+5 and above x-axis on the…

A: Fundamental theorem: To find the area under the curve y=f(x) between x = a and x = b, simply find an…

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

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Q: Find the area bounded by y = x² −1, the x axis, and x = 4 in the first quadrant using 6 divisions of…

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Q: Question in image along with part (a) repeated using left points and midpoints.

A:

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

A: Given problems:- a).  Estimate the area  under the graph f(x) =2x+1 from x=1 to x=2 using four…

Q: Find the area under the curve  y= (2x2 - 7) / (sqrt(x)) ,   16 <= x <= 20

A:

Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: 29. Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the…

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Q: Find the area, in square units, bounded by g(x)=3x−4 and f(x)=x2+5x−52 over the interval [−8,6]. Do…

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Q: Find area bounded by the carves. (Round answer to 2 decimal places) y = 7x² −2x _y=x³ -7x+4 +

A:

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: Estimate the area under the graph of f(x)=16−x2 from x=0 to x=4. Approximate using 4 rectangles.A.)…

A: Given function is Length of each rectangle is  Therefore, the interval [0,4] into sub-intervals…

Q: What is the area enclosed between the graphs of x=y2 and x=-3y+4? Round to the nearest hundredth.

A:

Q: Is it possible to get the area between y2 = 3x and y = x3, using  a. vertical strips b. horizontal…

A: Given  The equations are y2=3x  and  y=x3 .     Formula :- Area under the curve  a) vertical strip…

Q: Is it possible to get the area between y2 = 3x and y = x³, using a. vertical strips b. horizontal…

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

Q: 27. Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the…

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Q: Approximate the area between the curve J(x)=-x²+18x and the X axis on the interval 0, 18 |using 6,…

A:

Q: Find the area bounded between curves: (show the figure with the rectangular strip used)…

A: Given x2+42=16

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

A:

Q: Use the Left Endpoint method to approximate the area under the graph of the function f(x) = 9 In(æ³)…

A: Given interval is x=1 to 3 find out deltax using the interval △x=b-ana=1, b=3, n=8△x=3-18=14 Width…

Q: Find the area enclosed by the curves f(x)=38−x^2 and g(x)=x^2.

A: Solving

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.