Find f(x) dx for the function f(x) graphed below. [Hint: No calculus is necessary-just as we used integrals to find areas, we can use areas to find integrals. The curve shown is a quarter cirde.] 1. 2 3. 5 6 8

Q: 8(x) dx = 28(x) dx = 8(x) dx = L'18(x)I dx =

A: Given that, There is a graph and the area of parts is given. With the help of these areas and graph…

Q: 8 dx 2) Evaluate the integral Is x/x² – 16 Hint: Use a suitable u-substitution. You may find the…

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Q: f(1) = F + а. b. g(x)=In(x)e3r с. А(0)- sinh (0.50) k (x) = 2.x +1 x² - 2 d.

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Q: Given the function graphed below, evaluate the definite integrals. -t -2 -3 | f(2)dz = 0. | f(2)dz =…

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Q: B. Find the value of a such that the following function is continuous at every x Sx²-1, 2ах, x < 3…

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Q: Given the function graphed below, evaluate the definite integrals. -2 -3 f(x)dx = | F(z)dz -| to in

A: given,

Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: Q1 Consider the integral - dx . 1+x? (a) Draw the graph of f(x). (b) For which value of n the error…

A: The graph of the function is sketched below using online graphing calculator.

Q: 12. The area enclosed by the two curves y=x-4 and y =x-4 is given by (a) [(x-x)dx (b) [(x²-x)dx (c)…

A: y=x2-4  &amp;  y=x-4 The graph is,

Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 3. -1 -1 4 5 -2 -3 -4 |…

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Q: The graph shown below is f(x) = 3 sin x. What is the integral function g(x) that defines the area…

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Q: c) To evaluate this integral using the Fundamental Theorem of Calculus, I should find the [Select ]…

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Q: If f(1) = 14, f ' is continuous, and integral of 3 1 f(x) dx =17 what is the value of f(3)? f(3)

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Q: x´ + 7x between I = 1 Use the Fundamental Theorem of Calculus to find the "area under curve" of and…

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Q: Given the function graphed below, evaluate the definite integrals. 3. 2. 4 -2- -3 -4+ f(z)dz =…

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Q: Question 003: Complete the following question involving basic integration techniques. Given the…

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Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 -1 3 4 6 8 -2 -3 -4 | f(x)dx…

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Q: In each part, choose the letter from the dropdown menu that corresponds to the most accurate…

A: Differentiation: A.An antiderivative of y=-3That means integration of -3Therefore that will…

Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: Given the function graphed below, evaluate the definite integrals. 4 3. -1 1 2 3 5 -1 -2 -3 -4 1 |…

A: We have to find the value of the integrals.

Q: 2 Evaluate the definite integral S: 1 dx. 1 x+a2 ter -17 a- 19

A: solution:

Q: A light bulb manufacturer wants to produce light bulbs that last approximately 700 hours, but some…

A: b) Meaning of the derivative r(t) = F'(t) if rt = F't then ∫abrt dt represents the net change of Ft…

Q: 5. Let P(t) represent the population of fish (in thousands) in a lake. Suppose that the rate of…

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Q: Given the function graphed below, evaluate the definite integrals 4 -1 2 3 4 5 -2 -3 -4 1 | f(x)dz =…

A: Given-  To find- ∫19fx dx Concept Used-  An integral is a mathematical object that can be…

Q: -2 What is the value of the definite integral e* dx? -4

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Q: In the given question/s, (a) sketch the graph of the function, highlighting the part indicated by…

A: a)                      y=x2+x-2                               at x=-2,   y=-22+-2-2=0at x=-1,…

Q: Evaluate the definite integrals using the graph of f (x) below. 4- 2- 10 12 -2- -4- -6-

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Q: 48 (a) Evaluate the integral: dx x² + 4 Your answer should be in the form ka, where k is an integer.…

A: (a) Given information: ∫0248x2+4dx

Q: (c) Let ɛ be a number so that 1 > e > 0. Explain why the integrals dx, dx x2 -1 can be computed…

A: For (c), Let ε be a number so that 1&gt;ε&gt;0. Now, we will show why ∫ε11x2dx,   ∫-1-ε1x2dx can be…

Q: Given the function graphed below, evaluate the definite integrals. 4 2 6. 8. -1 -1 -2 -3 of -4 | =…

A: The integral of a function from one limit to another is the area under the graph of the function and…

Q: 1 1. (a) Estimate dx using L4. Is this an underestimate or overestimate of the value of the x +1…

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Q: 1 approximate Use linear approximation, i.e. the tangent line, to 1 as follows: Let f(x) and find -…

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Q: 10 le 4,0 10 A graph of f(x) is shown above. Using the geometry of the graph, evaluate the definite…

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Q: 2. Evaluate the definite integral below. 6 √x Enter your answer in exact form or rounded to two…

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Q: „10 "The substitution w = q° +3q² – q converts the integral f (q+3q² – q)" dq into fw" dw" Which of…

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Q: Given the function graphed below, evaluate the definite integrals. 2 3 4 5 6 7 8 -3 -5 [²ƒ(z)dz = −5…

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Q: - x2 + 9x between 6. In your calculations, if you need to round, do not do so until the very end of…

A: Area under curve = integration of function in respective given limits

Q: The function below has the form | f(x) dx. x2 dx (x³ – 1)1/3 (a) Evaluate the integral to obtain a…

A: The given function is  F(x)=∫x2(x3-1)13dx

Q: 1 secz The derivative of the function y at z = 1 is equal to Select one: O a.-1 b. Does not exist…

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Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: 54 x2 The integral I = 1 + dx is [Hint: You may need to use the Mean Value Theorem for Derivatives]…

A: We have to check the integral I is convergent or divergent with an interval.

Q: 0. Evaluate the following integral or state that it diverges: - dx (x+1)"

A: Definite integration

Q: Define a function L(r)=f (0)+xf' (0) for a functionf that is differentiable at x = 0. line at would…

A: Given function L(x)=f(0)+xf'(0) and differentiable at x=0

Q: 10. (a) Consider the integral dx. x² Why can't this integral be computed using the Fundamental…

A: Since there are multiple subpart the first three is answered.Kindly repost if any particular subpart…

Q: 5+ sin x dæ? 2 3. a) It can be shown to diverge by using the Comparison Test to compare it to 4 dx.…

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Q: 1. Find the distance traveled (to three decimal places) in the first four seconds, for a particle…

A: This is a problem related to integration of the function. B y integrating velocity we will get…

Q: 3 2x Estimate the value of the definite integral dx with n=4 subintervals, taking x+1 the sample…

A: Introduction: The endpoint formula and the midpoint formula are related. A midpoint is the point in…

Q: 3. The function f(t) is measured in miles per hour andt is measured hours. What are the units for…

A: If f(t) is measured in miles per hour and t is measured in hours A=

Q: Given the function graphed below, evaluate the definite integrals. 1 2 3 8 -1 -2 -3 of -41 2 |…

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Q: Given the function graphed below, evaluate the definite integrals. 4 -1 -- 5 6 -2 -3 f(x)dx 8 |…

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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.