What is the slope of the curve y = ex at x = ln 2? What is the area of the region bounded bythe graph of y = ex and the x-axis between x = 0 and x = ln 2?

Q: Find the area between y=x+2 and y= x2−1. Round your limits of integration and answer to 2 decimal…

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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: Suppose you want to approximate the area of the region bounded by the graph of f(x) = cos x and the…

A: Integration can also be defined as summation. Thus, integration can be used to calculate the area…

Q: The marginal revenue function has x measured in years and MR(x) in hundreds of dollars per year. Use…

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Q: Estimate the area under the graph of f(x) 1 over the interval [2, 6] using eight approximating x2 +…

A: A function is given by, fx = 1x2+4 over the interval 2,6. The objective is to find the area under…

Q: Approximate the area under the curve graphed below from 2 = approximation with 3 subdivisions. 1 to…

A: We can solve this using riemann integral

Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

Q: Other than using definite integrals,  how else can you solve areas of regions bounded by curves

A: According to the given information, it is required to tell what is the other way to calculate the…

Q: Find the area of the region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and…

A: The region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and x = 2 is as…

Q: What is the area under the curve of the following positive function y = 10x4 + 3x² between x = -1…

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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 curves y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A: Given curve: fx=x2+1 We have to find area under the given curve from x=0 to x=2. It is given that we…

Q: Estimate the area under the graph of f(x) 1 over the interval [0, 4] using eight approximating x + 4…

A: Given fx=1x+4. To find the area of f(x) over the interval [0,4].  Here, a=0 and b=4. Number of…

Q: The sum that best approximates the area under the curve between the function and x-axis on the…

A: our objective is to find the best approximation

Q: Estimate the area under the curve f(x) = 2x from 0 to 1 using R4. Leave your final answer as exact…

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Q: Find the indefinite integral ∫sech3 x tanh x dx

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Q: 1 Estimate the area under the graph of f(x) : x2 + 4 over the interval [- 1, 3] using ten…

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Q: 4. Approximate the area beneath the curve f¹, 2e-3x dx with n=4 subintervals. Round your answer to 3…

A: Introduction: Simpson's 1/3 rule is an approximation that is used when the number of sub-intervals…

Q: Find the area bounded by the curve f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

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Q: Approximate the area under the curve graphed below from x=2 to x = 6 using a Left Endpoint…

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Q: What is the area under the curve of the following positive function y = 10x4 + 3x2 between x = −1…

A: Given: y = 10x4 + 3x2 between x = −1 and x = 2 Area=∫-1210x4+3x2dx         =∫-1210x4dx+∫-123x2dx…

Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Consider the provided curve,  Bounded above by the curve y=ex2 and below by the curve y=e-x2. And on…

Q: Approximate the area under the curve of y =-x+ 5 on the interval [0,2] using a right hand…

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Q: Use the method of anti-derivative to find the area under the curve y = 4(x³ the interval [2,4]. 4x)…

A: Before finding the area, first, we will find the x-intercepts of the curve  to check that any point…

Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Estimate the area under the graph of f(x) : 1 over the interval [0, 4] using five approximating x +1…

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Q: Estimate the area under the graph of f(x) 1 over the interval [– 1, 4] using ten approximating x + 4…

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Q: Estimate the area under the graph of f(x) = 1 over the interval [0, 5] using eight x + 2…

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Q: Estimate (2x – 5) dx using midpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: 4

Q: Find the area between y=ln(x-6) and y = (ln(x-6))2

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Q: Approximate the area under the curve graphed below from x = 1 to x = 6 using a Left Endpoint…

A: The given curve is a parabola of the form, y2=4ax Since the curve passes through 2,2, it must…

Q: 1. Find the area of the region bounded from the right by the curve x = 4 - y2 , from the left by the…

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Q: Find the area of the region between the curve y = 6 3-X and the interval 0 sxs2 on the x-axis. 210…

A: Area under a curve: The area under a curve y = f(x) between the points x = a and x = b or over the…

Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Find the areas between the curves y = 2(log2 x)/x and y = 2(log4 x)/x and the x-axis from x = 1 to x…

A: To determine the area between the curves and the x-axis.

Q: 4. Use the right-endpoints and 3 subintervals to approximate the area of the region under the curvey…

A: Given curve is y=1/x We will divide the interval [1,4] into three sub-intervals. The length of each…

Q: 2 Set up the definite integral required to find the area of the region between the graph of y = 20 –…

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Q: Use integration by parts to evaluate the integral: ∫ln(x)/x^6 dx with upper limit of 4 and lower…

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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: Approximate the area under the curve y=3x between x=−2 and x=2 using Simpson’s Rule with n=4…

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Q: Calculate the area under the curve y between x = 2 and x 8. %3D

A: Since you have posted multiple questions therefore we will answer the first one for you. If you want…

Q: 2 Find the area between the curves y= 2x +6x+1 and y =-x +3x+7 over the interval [-4,10]. Draw the…

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Q: 5. Find the area under the curve integrate 2/(9 - x ^ 2) dx

A: Given;           ∫29-x2 dx Take the constant out: ∫a.fx dx=a.∫fx dx           =2.∫19-x2 dx Apply…

Q: Find the indefinite integral. (Use C for the constant of integration.) sech® x tanh x dx

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Q: Approximate the area under the curve 4=メ Right Endpoint from x=3 to メニの USing approximation with 6…

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Q: Estimate the area under the curve  y=(x+5)2-2 on the interval from x=0 to x=4.

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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: Approximate the area under the curve y=1/x from x=1 to x=4 using the left endpoint estimate with six…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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.