Let A(x) represent the area bounded by the graph.

Q: .Find the area under the graph of y = g(x) from -3 to 6, where x², g(x) = 18 – x, x > 2

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Q: Let f (x) = x° + 4x and g(x) = 6x² – X Determine the area A of the region enclosed by the graphs of…

A: We will find the area of the enclosed region.

Q: Plot the functions y1 : R → R, y2 : R → R given by y1(x) = x2 − x and y2(x) = x. Compute the area…

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Q: Find the area of the region enclosed by the graphs of f (x) = x3-x2 and g (x) = 2x

A: Given f(x) = x3 - x2   and g(x) = 2x The intersecting points of the functions are,  => x3 - x2 =…

Q: find the area bounded by x^2 = 4ay and a chord passing through its vertex

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Q: Find the area under g(x) = x−3/4 + 3x5/3 over [1, 3].

A: Integrations are used to calculate area under the curve as it becomes simpler when we use…

Q: Find the area bounded by the graphs of y = x + 2, y= -x, x= 0 and x = 1

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Q: Estimate the area under the graph of f(x)=1/x from x=1 to x=2 using left and right endpoints.

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Q: Find the area of the region under the graph of f on [a, b]. f(x) = 3/x^2 ; [1, 4]

A: To find the area of the region under the graph of f on [a, b]. f(x) = 3/x^2

Q: Sketch and find the area bounded by the graphs of y =÷-x and y =. 3

A: Use given curves draw the graph and find area

Q: Find the area generated by the graphs y=x4-2x2 and y=2x2

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Q: What is the area between the graphs of f (x) = 3x + 5, g (æ): -2x – 3, x = 2, and x = 12?

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Q: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

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Q: Use definition to find the area under the graph of f(x) = x² + x and above the x-axis on the…

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Q: Find the area bounded by the graphs of y = 3x2; x = 0; x = 2; and the x axis.

A: Given,

Q: Find the area of the region enclosed by the graphs of f(x) = x^3 and and g(x) = x^2+2x. %3D

A: Given that, the functions arefx=x3 and gx=x2+2x. Note that, the formula for area enclosed by the two…

Q: Determine the area bounded by y=x² and y=2- x2

A: Graph of the given functions helps to find the bounded area. Integration of the functions within…

Q: Find the area of the region bounded by the graphs of f(x) = 5 − x^2 and g(x) = x^2 − 3

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Q: find the area of the region bounded by the graphs of f(x)=x2 and g(x)=8x

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Q: Determine the area bounded by y²=x+1 and y=1-x

A: Solution of given question is written in below steps.

Q: Let a >1 be an integer. The area of the region bounded by the graphs of the functions y = 12ax and y…

A: This question is based on application of integration.

Q: The loop of y =x *(4 - x)

A: Here we have to find the area of the loop of y2=x4(4-x) ...................... (1)

Q: Find the area of the region under the graph of the function f on the interval [1, 5]. f(x) = 3x³…

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Q: 1. Sketch and find the area bounded by the graphs of y =-x x and y =

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Q: Find the area of the region bounded by the graphs of f(x) = x³ – 3x + 2 and g(x) = x + 2.

A: Given functions are fx=x3-3x+2,gx=x+2. Graph the given functions as shown below. From above graph,…

Q: Find the area of the region enclosed by the graphs of f(x)=x'-x and g(x)= 2x. %3D

A: The given functions are fx=x3-x2  and  gx=2x

Q: Find the area of the region under the graph of f on  [a, b]. f(x) = 6/x^2 ; [4,5]

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Q: Find the area under the split-domain function from x = -2 to x = 3.

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Q: Find the area of the region bounded by the graphs of f(x) = 2 - x2 and g(x) = x.

A: f(x)=2-x2, g(x)=x

Q: find the area bounded by the graphs: y=x^2-3 and y=2x

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Q: 1. Sketch and find the area bounded by the graphs of y =-x and y=

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: a) Estimate the area under the graph of f(x) = 6/x from x = 1 to x = 5 using four approximating…

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Q: Find the area bounded by the curves f(x) =x and g(x) =x4

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Q: Find the area of the region bounded by f(x)=-x^2+1, g(x)=2x+4, x=-1, and x=-2.

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Q: Determine the area bounded by g(x)=x^3-4x+7 and h(x)=x+5

A: To  find Area bounded by g(x)=x3-4x+7 and h(x)=x+5

Q: What is the area between the graphs of f (x) = 3x + 5, g(x) = -2x – 3, x = 2, and x = 12?

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Q: find the area enclosed between f (x) = 0.6x² + 5, g(x) =x, X=-5 , x = 6

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Q: Find the area of the region bounded by the graphs of f(x) = -x² + 2x +5 and g(x) = |2x|.

A: Here we have to find out the area bounded by the given curves.

Q: Find the area of the region R under the graph f (x) = x^2 on [0, 1]

A: Find the area of the region R under the graph f (x) = x2 on [0, 1] .

Q: %3D y = x²– 2x

A: Here we have to find the area bounded by the curves y=6x-x2 ............... (1) and y=x2-2x…

Q: 5. Find the area bounded by the graphs of f(x) = x2 – 3x – 10 and g(x) = x + 2 %3D -

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Q: Determine the area bounded by g(x) = x³ – 4x + 7 and h(x) = x + 5. %3D

A: Two functions are given

Q: Determine the total area bounded by the functions f(x)=-x2+2 and g(x)=x3-x2-x+2.

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Q: 1. Sketch and find the area bounded by the graphs of y =-x and y =

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Q: Find the area A of the region between the graphs of f and g on the interval [1/2, 2]

A: It is given that fx=1x,gx=1x2 and the interval is 12,2. Recall the fact that the area of two curves…

Q: Find the area bounded by Y1=X2, Y2=X, X=0 and X=2 graph it and show ALL

A: Consider the graph:

Q: Let f (x) = x3 + 5x and g(x) = 7x2 − x Determine the area A of the region enclosed by the graphs of…

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Q: Exercise 9. Find the area bounded by the graphs of functions y = x°, y = 8, x = -1.

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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.