find the total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

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: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

A: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

Q: Use integration by parts to evaluate xedx

A:

Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

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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 of the region bounded by the graph of f(x) = x² + 1, the x-axis and the vertical lines…

A: Explanation of the answer is as follows

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) = 4 over the interval [2, 5] using five approxima %3D…

A: Given: f(x)=4x

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 under the graph of f(x) = 36 – x² over the interval [ – 6, 4] using eight…

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Q: Estimate the area under the graph of f(x) = 16 - r² over the interval [- 4, 1] using ten…

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Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

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Q: Describe the Mean Value Theorem for Integrals in your own words?

A: The mean value theorem for integrals declares that somewhere between the circumscribed and inscribed…

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: 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 distance between the point (-1,2) and the line with x-int 1/3 and y-int 3/4.

A:

Q: There is a line through the origin that divides the region bounded by parabola y=x-x^2 into two…

A: Given There is a line through the origin that divides the region bounded by parabola y=x-x^2 into…

Q: Evalute the indefinite integrals using the general power rule

A: ∫5e3x9-12e3x+4e6x4dx

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

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Q: Estimate the area under the graph of f(x) = x² + 2x + 1 over the interval 1, 6 using four…

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Q: Using left endpoints, approximate the area under the curve of f(x) =3x^(2) + 1 over the interval [0,…

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Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 2 using left sum with two…

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Q: Find the area of teh region bounded by y=5x/x2+2, x=1, x=5, y=0. Sketch the graph

A: We graph the region using a graphing calculator.

Q: ded by the curve or line: y2+4x-8=0, Y

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: Estimate the area under the graph of f(x) over the interval [0, 3] using five x + 2 approximating…

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

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

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Q: Estimate the area under the graph of f(x)=9−x2 over the interval [−2,3] using five approximating…

A: The width of the interval [-2,3] is = 3-(-2)=5So the width of each sub-interval=∆x=55=1So the…

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

A: a = 0; b = 4; n = 4; Width = Δx = (b - a) / n = (4 - 0) / 4 = 1

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

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Q: Find the area bounded by the curve y= 2x-3/x2+4, the coordinate axes and the minimum ordinate. Show…

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Q: The total area bounded by the graph of y = 5 - x, the line a x = 0 and the x-axis

A:

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

A:

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

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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: Estimate the area under the graph of f(x) = over the interval [– 3, 0] using four x + 4…

A: The function is given as, fx=1x+4 It is also given that, Number of rectangles, n=4Upper limit,…

Q: area bounded between y=3x+2 and y=-x^2+2

A: here we have to find the area bounded between the curve y=3x+2......(1) and y=-x2+2x+4.....(2)

Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 4 using right sum with two…

A:

Q: Estimate the area under the graph of f(x) = x + 3x +1 over the interval [2, 4] using eight…

A: Given function fx=x2+3x+1 over interval [2, 4] and number of sub intervals, n=8. ∆x=b-an=4-28∆x=14…

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

A:

Q: Estimate the area under the graph of f(x)=36−x2f(x)=36-x2 over the interval [−5,2] using five…

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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: Determine the area bounded by the curve y = x2 - 3x -6 and lines y =-4-x,x = 0 and x = -2.

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

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

A: Given :  Function f(x) = √(x+3), Interval [-3,1], To find : Area under the graph of given function…

Q: Estimate

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.