Consider the region, R, bounded above by f(x)=x2+10x+25 and g(x)=9x+81 and bounded below by the x-axis over the interval [−9,−5]. Find the area of R. Give an exact fraction, if necessary, for your answer and do not include units.

Q: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

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Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: What is the area (in square units) of the region bounded by the graphs of y=x²+2, and the x axis…

A: Area under the curve is given by integration over required interval

Q: 4. Find the area of the region bounded by the graphs of f (x) = x³ +x2 – 6x and g(x) = 2x – x2 20 А.…

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Q: Find the area of the shaded region. 1) f(x) = x3 + x2 - 6x %3D 30+ g(x) = 6x 20- (3, 18) 10+ (0:0)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a. Find the area below f(x) = -x² + 4x + 3 and above g(x) = -x³ + 7x2 – 10x + 5 over the interval 1…

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Q: find the area of the region bounded by the functions f(x)=−13x+2 and g(x)=2x−1 over the interval…

A: The given functions are: fx=-13x+2, gx=2x-1 over that interval -2,1 Calculate the area of the region…

Q: Consider the region bounded by the graph of y = 4x + 3, the x-axis, and the lines x = 2, x = 7. A…

A: Given area bounded by the curve y=4x+3, x-axis and the lines x=2, x=7

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: Determine the area, in square units, of the region bounded by f(x)=10x3+x2−21x−9 and…

A: The region bounded by the curves, fx=10x3+x2-21x-9 and gx=9x3+x2-5x-9 over the interval [2,6].

Q: Find the area of the region between v= 4x - x2 and the x-axis from x = 0 to x = 4. 11 square units O…

A: Area of region can be determined using the formula given as     A = ∫ba y dx   ........(1)…

Q: Find the area of the region bounded by the graphs ofy = x² - 4 and y =r+2. Give your answer as a…

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Q: Find the area of the region bounded by the graph of f(x) = 4 − x2, the x-axis, and the vertical…

A: Given curves: The graph is:

Q: Find the area between f(X)= -x2+4x and g(X)=x2-6x+5 over the interval 0 ≤x≤ 1. sketch the region

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Q: . Find a number k > 0 such that the area of the region bounded by the curves y = x², and y =k – x2…

A: As per as our guide line I am supposed to answer only one question from these 2 question Please…

Q: In finding the area between the regions y = x2 – 2x and y = - x, the limit values of x are О а. 1, 1…

A: The given curves are y=x2-2x and y=-x.

Q: Find the area of the region bounded by the graph of ​f(x)=sin x and the​ x-axis on the…

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Q: Determine the area, in square units, of the region bounded by g(x)=−7x−7 and f(x)=x2 −11x−28 over…

A: To calculate the area bounded between the curve g(x)=-7x-7 and f(x)=x2-11x-28 over the interval…

Q: f(x) = 3. 2. 14

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Q: Determine the area, in square units, of the region bounded by f(x)=−7x3−4x2+2x−1 and…

A: To find the area bounded first find the intersection of f(x) and g(x)

Q: Find the area of y=4ex/1+e2x bounded by the x-axis, y-axis and line    sketch the graph

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Q: Find the area of the region enclosed between f(x) = x² +4x + 8 and g(x) = 2x² – 1x + 2. Area = %3D

A: To find the area of the region enclosed between the curves fx=x2+4x+8 and gx=2x2-x+2, first, find…

Q: Determine the area, in square units, of the region bounded by f(x) = 10x³ + x² - 21x - 9 an g(x) =…

A: To determine the area, in square units, of the region bounded by fx=10x3+x2-21x-9 and gx=9x3+x2-5x-9…

Q: Determine the area, in square units, of the region bounded by g(x)=−10x+11 and f(x)=x^2−5x−13 over…

A: Solve the following

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x² - 6x + 13; [−1, 2]

A: To find the area of the region under the graph of f(x)=x2-6x+12 on the interval [-1,2].

Q: If R is the region bounded above by the graph of the function f(x): = x + 4 and below by the graph…

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Q: Determine the area, in square units, of the region bounded above by f(x) = -x² + 20x – 70 and below…

A: Given:  fx=-x2+20x-70 gx=x+20 To find: Find the area over the interval 9, 10. Required formula:…

Q: Find the area of the region enclosed between f(x)=0.2x^2+10, g(x)=x, x=−7, and x=2.

A: Given curve is: fx=0.2x2+10gx=xx=-7x=2 To find the area of the region enclosed between the curve.

Q: Find the area of the region bounded by the y-axis, the line x = 3, and the functions f(x) = 1/2 (x^2…

A: Consider the functions fx=12x2-3x+10 and gx=-13x-1 Find area of region bounded by the y-axis x=0 and…

Q: 1. Find the area bounded by y2 = 4a(y – x), y² = 2a(x + 2y – 3a) and the x-axis.

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Q: Determine the area, in square units, of the region bounded by f (x) = –3x³ + 3x² + 24x - 4 and g(x)…

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Q: Find the area of the region between the graphs of y = 15 – x² and y = - 3x + 5 over the interval 0 <…

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Q: If R is the region between the graphs of the functions f(x) = 4x + 9x2 + 7x – 3 and g(x) over the…

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Q: 2 3. Find the area of the unbounded region between the x-axis and y=- for x26. (x-4)

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Q: Find the area bounded by the curve c²y=x³, the x – axis, and the line x =2c.

A: We find the area bounded by the curve using the integration. Before finding the area, first, we will…

Q: the and g(X)=x²-6x+5 sketch the region over the interval 0 sxs 1.

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Q: The area of the region bounded by the graphs of f(r) 2– a and g(x)=r is A-

A: Here we will find out the required value

Q: Find the area of the region enclosed by x = y² – 4y + 2 and x = y - 2.

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Q: Consider the region, R, bounded above by f(x) = x² – 6x + 9 and g(x) over the interval 3,9. Find the…

A: Consider the given information,

Q: Determine the area, in square units, of the region bounded by g(x)=6x+12 and f(x)=x2 +7x−8 over the…

A: We have to find the area under the curve of g(x), then substract the area under the curve of f(x).…

Q: Find the area of the region enclosed between (x)=x^2+5x+9 and g(x)=2x^2+3x+1

A: We have to find the area of the region bounded by curves f(x)=x2+5x+9 and g(x)=2x2+3x+1. The region…

Q: Find the area of the region bounded above by y = -x2-3x-2 and below by y = -2. AY 51 4 3 54 32 t 1 2…

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Q: Determine the area, in square units, of the region bounded by f(x) = 2x³ + 5x² – 11x + 9 and g(x) =…

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Q: Find the value of c > 0 such that the area of the region bounded by the parabolas x² - c and c2 -x²…

A: Sketch the region and integrate in x variable.

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: Consider the region, R, bounded above by f(x)=x5^2−6x+9 and g(x)=−3x+27 and bounded below by the…

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Q: Find the area of the region bound by the x-axis, f(x) = sin x, x = -. 3' TT and x = 2

A: The equation of the curves are : C1 : fx = sinx C2 : y = 0 C3 : x =-π3 C3 : x =π2 To evaluate : The…

Q: Find the area of the region bounded by the graphs of the given equations. b) f(x)=2x2-6x+5,g(x)=x2+…

A: See below the answer and calculation

Q: Area under the curve?

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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.