5) Sketch the graphs of the functions f and g. f(x) = x2, g(x) = 1/x2   Find the area of the region enclosed by these graphs and the vertical lines x = 1 and x = 3.     = ? square units

Q: 6. Find the area of the region enclosed by the graphs of y = Vx+1 and y = }x – 2 and the vertical…

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Q: 26 Find the area of the region bounded by, c. The curve y= In x, the lines x 4 and the x-axis. d.…

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Q: 2. Find the area between the curves f(x)=3-x and g(x)=1-x. Provide a sketch and shade the region…

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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: topic - area under the curve

Q: Sketch the function y = x on the interval [0, 2] and let R be the region bounded by y = x and the…

A: Given function is y=x on the interval [0,2]   As we know, The area bounded by function interval…

Q: 2) a) Consider a rectangle which is on the region bounded by the lines y = x+4, y =-x+4 and X -…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Graph of the function y = cos 2x What is the area of the region bounded by the x = 15°, x = 45°…

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Q: 2. An area is bounded by the curve y = 8/(x² + 4), the x-axis, and the lines x + 2 = 0 and x-2 = 0.…

A: Given, The curve bounded by y =  8/(x2+4) and x axis (y=0) And lines x+2=0 and x-2=0 x= -2 and x=2

Q: Find the region bounded by the graphs of the equations : りミメき,リ:タx

A: Let's find.

Q: 19) The region in the first quadrant bounded on the left by the circle x2 + y2 = 1, on the right by…

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Q: Sketch the region bounded by the graphs of the functions. y = 25 - x, y- x2 - 11x + 50, x = 0 60 50…

A: We first sketch the region using a graphing calculator.  The first option matches this graph.

Q: 5.(b) On the same axes, sketch the graphs of both g(x) and h(x), clearly labelling the coordinates…

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Q: 7. Find the area of the region bounded by the graph of y= 2x-3x+2, the x-axis, and the vertical…

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Q: 3. Sketch the graphs of the curves y = 2x² + 1 and y=7-x. Shade the region bounded by the curves.…

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: 2. Find the area of the region R enclosed by the curves given by the graphs of f(x) = v3x, g(x): =…

A: Area between curves

Q: Find the area of the region enclosed by the graphs of the functions f(x) = 2e*, g(x) = -x +2 %3D and…

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Q: Find the area of the region that is bounded above by the curve f(x) = sqrt(x−7) and the curve g(x) =…

A: The given curves: fx=x-7 and gx=19-x.The area is bounded by the above curves and x axis.

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: Sketch the region bounded by the graphs of the functions. f(x) = e0.25x,    g(x) = −  1 x,    x = 1,…

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Q: 3 Find the area between the graphs of f(x) = x', g(x) = x' and the linesx = 0 and x- 2 + g(r) Find…

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Q: Find the area. of. the region.. R. bounded by the graphs.of gilen equations I, 4=1-x X= 0 and x=2…

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Q: 65. The region bounded by f(x) = x² and the x-axis on the interval [1, 0) is revolved about the…

A: We have to find the volume of the described solid of revolution.

Q: Sketch the region bounded by the graphs of the given equations and find the area of that region.…

A: Area between curves

Q: 7. Find the area bounded by the two curves, f (x) = x and f (x) = x + 2 between x-0 and x=2. Hint:…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the area of the region bounded by the graph y = sin x, y = 0, x = 0 and x =3π/2

A: Area of a region when strip taken parallel to y-axis is ∬dydx.

Q: .2 What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis…

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Q: Sketch the region bounded by the graphs of the equations f(x) = 3√x − 1,   g(x) = x − 1 and find the…

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Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

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Q: Find the area bounded by y = 5 + 2x -x2 and the chord passing through (-2, -3) and (3, 2). Sketch…

A: Let us consider two curves f(x) and g(x) [continuous functions] such that f(x)≥g(x) in the interval…

Q: 17.Find all points where the curves y = 3r and y = r - r intersect, by solving an appropriate…

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Q: Find the area of the region completely enclosed by the graphs of the functions f and g, where f > g…

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Q: 2. Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -X.

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Q: Find the area of the region bounded by the graphs of the equations. 9 x = 1, x = e, y = 0 x

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Q: calculate an area of ​​the region bounded by the curves   f(x)=x³+2x-1 and g(x)=3x-1

A: the given curves are     to find the bounded region first we have to identify the intersection…

Q: Determine the area enclosed by the curves y=-x² + 4x and y =-x +4. Draw a sketch of the graphs on…

A: The given curves are: y=-x2+4x and y=-x+4

Q: Find the area of the region completely enclosed by the graphs of the functions f and g, where f > g…

A: Given: The function fx=-x2+4x and gx=2x-8, To find: The area of the region completely enclosed by…

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

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Q: Find the area between the curve on the given interval  y= x^3 , y= x^2-1, 1 < x < 3

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Q: Sketch the region bounded by the graphs of the equations f(x) = 10 / x ,         x = 0, y = 2, y =…

A: Sketch the region bounded by the curves y=10x,  x=0,  y=2   and  y=10 as shown below.

Q: Find the area of the region enclosed between f(x) = 0.8x+ 10, g(x) = x, x = -7, and r = 8 Area =

A: Given, f(x)= 0.8x²+10 g(x)= x x=-7 and x= 8

Q: 6. Find the area of the region bounded by the graphs of f(x) = 2 - x and g(x) =x.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: Find the area bounded by the x-axis, the curve y = x² and the vertical line x = 3. and Find the area…

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Q: Find b such that the line y = b divides the region bounded by the graphs of the equations into two…

A: Given: y = 9 - x2,  y = 0 To find: The value of b such that the line y = b divides the region…

Q: Find the area of the region bounded by (1/(x^2)) – 1, the x-axis, between x = ½ and x = 2. Your…

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Q: Determine the area enclosed by the curves y =-x + 4x and y =-x+4. Draw a sketch of the graphs on the…

A: The shaded region represents the region enclosed by the given two curves.

Q: (1) Theorem: The area A of the region bounded by the curves y = f(x), y = g(x), and the lines x = a,…

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Q: Find the area of the region completely enclosed by the graphs of the functions: f(x)=x^3-8x+3 and…

A: fx=x3-8x+3 gx=x+3 find the intersection points x3-8x+3=x+3 x3-8x+3-x-3=0 x3-9x=0 xx2-9=0 xx+3x-3=0…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.