Consider the following. y 16 | y = f(x) 16 (a) Use six rectangles to find estimates of each type for the area under the given graph of f from x = 0 to x = 24. (i) Sample points are left endpoints. (ii) Sample points are right endpoints. (iii) Sample points are midpoints. M6 %3D

Q: How many individual areas in the total area bounded by the curve y=x - 3x +2x and by the x-axis from…

A: first we plot the given region then decide how many areas exist

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x – x² and the x-axis.

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

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Q: 15) When does S, f(x) dx represent the area under the graph of f (x), above the x-axis, between x =…

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Q: Find the area below the x-axis and bounded by the curve  y=1-2x for 5<=x<=7.

A: The given curve is: y = 1 - 2x;  where 5 &lt;= x &lt;= 7 The graph is as follows:

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

A: In this Question I we taking the endpoint mid point and finding values

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: 3 Estimate x dx using right endpoints for n = 4 approximating rectangles. x² dx is approximately

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Q: * Example (6): Find the area between the curve x = y² and the line x = y + 2 Solution :

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Q: Q4. Find the area between curve y = x - 3x + 2 and x-axis from x =0 to x 2

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Q: 6. Find the area between the curve y = x(x - 3) and the ordinates x = 0 andx = 5.

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Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Using a left sum with n=3 rectangles to estimate the area above the x-axis and under the curve…

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Q: The area between y = x and r-axis on the interval -1, 1 with right endpoint rectangles is O…

A: We need to choose correct option.

Q: Find the area between the graph of x = and the y-axis on the interval [1, 4]. 4 3 2- 1 0.5 05 1 1.5…

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Q: 1. Find the area in the first quadrant bounded by f (x) = 4x - x and the x-axis. %3D

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Q: Q4 Find the area of the bounded by the curve and the x-axis. [2] S(x) = 4 – x²

A: Topic:- area under the curve

Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: Solve for the area beneath the curve y = -(x – 1)² + 10 and above the axis from x = -1 and x = 2.

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

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

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Q: The area under flx) between X=L and x=2 fal= 3x2

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Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

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Q: If L2 is the sum of the approximating rectangles for the area under the curve y = | cos x| from 2n…

A: Solve the following using left end points approximation

Q: Find the area between y = (x - 3) eX and the x-axis from x = 3 and x 9.

A: Give that

Q: 22) Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2 sxs2 of the…

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Q: 4.1 Can you show me all the steps to solve problem 5?

A: (a) Draw the graph for the function with three rectangles using the right endpoints as shown in…

Q: 7. Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line p through the…

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Q: Example: Find the area of the region in the first quadrant that is bounded above by Y1 =Vx and below…

A: The graph is shown below:

Q: Find the area of the region under the graph of the function f on the interval [-2, 1]. f(x) = -x2 +…

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

A: Given function is  We divide the interval [0,4] into four sub-intervals and length of each…

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x- x and the x-axis.

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

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Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

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Q: Find the area the region lying between the x axis and the curve y=(ln(8x)-1)/x2 to the right of the…

A: Given curve is y=ln(8x)-1x2 Since region lying between x-axis and the curve to the right of the line…

Q: c) [1 graph of : Estimate the area under the f(x) = x² + 1 from x = 0 to x = 2 using four…

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Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

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Q: Find the total area between the curve of the function f(x)=−2x and the x-axis over the interval…

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Q: 5. Find the area of the region that is enclosed by the graphs of the functions: y=-x? - 3x + 4 and…

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Q: Consider the function f (x) = x² + x + 2. What is the maximum approximation of the area under the…

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Q: Solve. 1. Find the area of the region between the function f(x) = 4x + 1 and the x– axis on the…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x? – 3x + 229, where x…

A: Given C(X)=0.01x2-3x+229      And R(X)=429-2x Where X is the number of cell phones

Q: The area under the curve y =3/x over the interval [1.4]is equal to: 14

A:

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

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.