Which of the following represents the area bounded by the graphs of f(x) = −x3 + 12x and g(x) = x2

Q: (a) Estimate the area under the graph of f(x) = 7 + 2x2 from x = -1 to x = 2 using three rectangles…

A: Given:- Estimate the area under the graph of f(x) = 7 + 2x2 from x = - 1 to x = 2  To find:- using…

Q: Determine the area of the given region. 1. Region between f(x) = x - 3x – 4 and the x-axis from x =-…

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Q: 1. Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis. f(x) = 4x-x² 3 2 3 1 2…

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Q: Let A be the area of the region that lies under the graph of f(x) =e -x  between x =0 and x =2

A: The diagrammatic representation of the area is,

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x – x² and the x-axis.

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Q: Find the area under the graph of f(x)= x2 and above the x-axis, between x = 0 and x = 3.

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: Below is the graph of y = x +5. 20- 15 10- -4 -3 -2 -1 0 1 The area bounded by y = x +5 and the…

A: Given problem:- Find The area bounded by y= x2 +5 and the x-axis from  x=-3 to x = -1

Q: Find the area under the graph of f over the interval [3,8). 4x + 5, for xs6 f(x) = - 35 - x, for x>6

A: As per the Guidelines, I can solve only first question. For second question, please post the…

Q: find the area between f(x)=x2+2 and g(x)=-x+1 on [1,3]

A: Draw the graph. To find the region between the red and blue function: Red: y=x2+2 Blue: y=-x+1…

Q: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

Q: Find the area under the graph of g over[-2,3]. (x2 + 4, for xs 0, 3. g(x) 4 - x, for x>0 -x2 + 5,…

A: A function.

Q: d the area bounded by the graphs of x = y² and x 2 - y²

A: Topic = Area

Q: Find the area of the region under the graph of f(x) = ln(x) from x = 3 to x = 11.

A: Given function : f(x) = ln(x) To find the area of the region from x=3 to x=11 To find the area of…

Q: Find the area bounded above the graph of the function f(x) = 9-x2 /4 and below the graph of the…

A: We first sketch the region using a graphing calculator.  The x coordinates of the intersecting…

Q: Let f(x)=3x°. /16 – x* - The area between the graph of f and the x-axis, on the interval [0,2] is..

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Q: 2) Find the area of the function f(x)=x² +4 for x=-1 tox=4.

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Q: Say the function g(x) = ;x + 2. Approximate the area bounded by the graph of y = g(x) and the x axis…

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Q: The area under the graph of f(x) = 3x2 between x = 2 and x = k is 208, where k> 2. Find the value of…

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Q: 2. Suppose that when the area A between the graph of a function y = f(x) and an interval [a, b] is…

A: Given that,  Function y = f(x) and interval [a,b] is approximated by the areas of n rectangles.…

Q: Compute the area between the x-axis and the graph of f(x)=x(x-1)(x– 2) on [0,3].

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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: Below is the graph of y = x2 +5. 20- 15 10- -4 -3 -2 -1 2 The area bounded by y = x2 + 5 and the…

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Q: Consider the following. f(x) = x(x² – 11x + 35) x2 g(x) %D (a) Use a graphing utility to graph the…

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Q: Find the area under the graph off over the interval [1,4]. x+7, for x ≤2 f(x) = 11-x, for x>2 The…

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Q: Find the area under the graph of f(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

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Q: 1) Find -x° +7x- 10x +3 over the interval 1s XŹ2 (Drow and illustrate the graph). the area below f…

A: Here we will find area above f(x) and below g(x),

Q: Find the area of the region enclosed by the graphs of f(x)=x²-10x and g(x)=6x 50-64

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Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

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Q: Find the area of the region enclosed between f (x) = x2 + 6x + 13 and g(x) = 2x2 + 2x + 1. Area =…

A: We need to find out intersection points pur f(x) = g(x)

Q: Find the area of the region bounded by the graph of f and the​ x-axis on the given interval.…

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Q: 1. Find the area bounded by y = -x' - 3x and y =- 4. |

A: solve the following

Q: 1 75. Find the area of the region bounded by the curve f(x) = (16 + x²)-3/2 and the x-axis on the…

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Q: The area under the graph of f(x) = 3x2 between x = 2 andx = k is 504, where k > 2. Find the value of…

A: Given

Q: 2. Find the area between the graphs of the functions f(x) = 8 – 2a2 and 9(x) = 4 – x? over the…

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Q: 1. Graph the function f (x) = x² - 1 and show by shading the area under this curve between x = 1 and…

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Q: Consider a graph of f(x)=x3−2x2+2 and f(x)=x. Find the area of the region bounded between the curves…

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Q: Find the area of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

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Q: Find the area of the region enclosed between f (x) = 0.1x2 + 4, g(x) = x, x = -8, and x = 4

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Q: Find the area bounded by f(x) = -x² +4x +1 and g(x) =x+1

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

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 below f(x) = -x? + 4x +3 and above g(x) = -x +7x² – 10x + 5 over the interval 1šx52.

A: The given two curves are  f(x) = y = - x2 + 4x + 3 g(x) = y = -x3 + 7x2 -10x +5

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: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: Find the area of the region lying under the graph of f(x) = √4 x from x = 1 to x = 16.

A: It is given that,                 f(x)=4x from x=1 to x=16We have to find the area of the region…

Q: 2. Find the area bounded by y = 4x – x² and the x – axis. · Solve in two ways.

A: Solution:Giveny=4x-x2   and x-axisTo find the area of the bounded region.Formula:Area=∫abydx

Q: Find the area of the region bounded by the graphs of the algebraic functions. f(x)=x^2-14x g(x)=0

A: SOLUTION-

Q: 5. Find the area of the region between the graphs of f(x) = x3 – 2x2 + x - 1 and g(x) = -x2 + 3x -…

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x over the interval 0, 3 by using…

A: The given function f(x)=9-x2 over the interval [0,3]

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.