Find the area of the region R bounded bythe graph of ƒ and the x-axis on the given interval. Graph ƒ and showthe region R.ƒ(x) = (1 - x2)-1/2 on [( -1/2),√3/2]

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: 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: Find the area of the region bounded by the graph ofy =1/x the x-axis, and the vertical lines x = 1…

A: The area is calculated by taking a rectangular element of width  dx and height y. The total area is…

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: Find the are of the region under the graph of f on [a,b] f(x)=e-x/2 ; [-1,14]

A: Given, fx=e-x2,           -1≤x≤14 Since fx is continuous and positive on the interval -1,14, area…

Q: In the given question , use the Midpoint Rule with n = 4 to approximate the area of the region…

A: We have to use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the…

Q: If R is the region between the graphs of the functions f(x) = 8x³ + 7x² + 28x + 6 and g(x) = 7x³ –…

A: Plot the curves f(x) and g(x) and find the region bounded by the curves over the interval [ -2,2].

Q: Find the area of the region between the graphs of the functions f(x) = -Vx and g(x) = 2 - x on [3,…

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Q: Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4], then find the area of…

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Q: Suppose we want to know the area of a region that is bounded by the graph of F(X)=1/2x+2 and the…

A: Consider the given curves.

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: Which of the following represents the area of the region bounded between the graphs of y= x² + 3x…

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Q: Find the area of the region between the graphs of the functions f(x) = -Vx and g(x) = 2 – x on [3,…

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Q: Find the area of the region bounded by the graph of g(x) = (x − 4)^4 and the x-axis between x = 2…

A: From the given curves

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 enclosed by the graphs of f(x)=x²-10x and g(x)=6x 50-64

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Q: Find the area of the region enclosed by each group of curves. ƒ(x) = x2 - 4x, g(x) = x - 6

A: We find the intersection points of f(x) and g(x) as, x2-4x=x-6⇒x2-4x-x+6=0x2-5x+6=0⇒x-2x-3=0⇒x=2, or…

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 of the given region. 3. Region between f(x) = x - 4x and g(x) = x.

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

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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: Find the area of the region bounded by the graphs of y2 = 5 – x and y2 = 4x.

A: Given y2=5-xy2=4x

Q: 1. Find the area of the region bounded by f(x) = x, the x-axis, and the vertical lines x = 0 and x…

A: Given: 1.f(x)=x3  x=0 and x=1

Q: 3. Find the area of the region bounded by the graphs of y = 2 - x² and y = -x. 4.5 O 1.5 O -1.833…

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Q: Find the area of the region under the graph of f (x) over the interval (1,8).

A: Given: fx=12x23; x∈1,8 for finding area of the region under the graph of given function on given…

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

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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 of the region bounded by thegraph of ƒ and the x-axis on the given interval.Ƒ(x) = x2…

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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 region under the graph of f on [a,b] f(x) = x^2 -8x +18 ; [-1 , 2 ]

A: The area under the curve is given by:

Q: Consider the graph of f (x) = –x² + 3x + 2. Estimate the area of the region bounded by the graph of…

A: Given  f(x) = -x^2+3x+2

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: 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: 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: Find the area of the region under the graph of f(x) = In(x) from x = 7 to x 14.

A: Here we find the area of the region under the graph of f(x)=ln(x) from x=7 to x= 14 so, we use…

Q: Find the area of the region between the graph of f (x) = x* – 3x² +8 and the closed interval [-1,…

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Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) =1/x…

A: To Find  The area of the region bounded by thegraph of ƒ and the x-axis(y=0) on the given…

Q: Find the area of the following regions.The region bounded by the graph of ƒ(x) =x/√(x2 - 9) and…

A: Given: The region is bounded by the graph of f(x)=xx2-9 and the x- axis between x=4 and x=5.

Q: Find the area of the region between the x-axis and the graph of f (x)= x' – 4.x² + 3x, Osxs2. .

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Q: 1D GRAPH the bounded by yox'lNx, yeo, regloN メ=, x='3 región AND FiNd the area of the

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

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: 53. Sketch the region under the graph of f(x) = 1+x2 for -00 < x < 00, and show that its area is I.

A: To sketch the region under the given graph and show that the area is π.

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: -. Find the area of the region between f(x) = 1-x² and g(x) = x + 3 on the interval [-2,2] 0 2

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Q: 2. Find the area of the region bounded by f(x) = 3x³ - x² - 10x and g(x) = 2x – x². %3D

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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: Find the area of the region under the graph of the function f on the interval [3, 7]. f(x)=6ex -x

A: To find the area of the region under the given function on the interval [3,7].

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.