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

Q: Find the area of the region between the graph of y=x+2, above x-axis, and between the lines x= -1…

A: Given:

Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y-3 0.

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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…

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Q: Find the area of the region bounded above by y AY -x² + 8 and below by y = x². ==

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Q: Find the area of the region between the graphs of y = 16 – x and -1< x < 7. 3x 2 over the interval…

A: Given: The functions y=16-x2 and y=-3x-2, To determine: The area of region between the graph of…

Q: What is the area of the region between the graphs f (x) = 3x – x and x – axis from x = 0 and x = 2 2

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Q: 4. Find the area of the region bounded by the graphs of y = x3 + 6x, x = 0, x = 2, and the x-axis.

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 10x, y = 0

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Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: Find the area of the region bounded by the graphs of the equations: f (x) = V5x – 10 g(x) = 2x – 4

A:

Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

A: Given equation y=-x2+6x,  y=0. The objective is to find the area of the region. "Since you have…

Q: Find the area of the region bounded by the graph of y = x /(x2 + 1) the x-axis, and the line x = 3

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Q: Find the area of the region enclosed between f(x) = x² + 4x + 12 and g(x) = Area = | 2x² + x + 2.

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Q: Find the area of the region bounded by y = -x² – 4x – 2 and y = 2x2 + 8x + 7.

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Q: Find the area of the region bounded by y=0 and y = -5x + x6

A: We first sketch the region using a graphing calculator

Q: Find the area whose region is bounded only by the graphs y + 1 = - x^2 + 7, and y - 3 = ( x - 2 )^2…

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Q: Find the area of the shaded region. f(x) = 10x – 3x - x°, g(x) = 0

A: We have to find the area of the shaded region. f(x) = 10x-3x2-x3,  g(x) = 0   The graph is

Q: Find the area A of the region R between the graph of f(x)= (x^2)/(4-x^2)^(1/2) and the x-axis on the…

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Q: Find area of the region. f(x)=x2-8x g(x)=0

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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: function f(x)=4-x2 To find area of region bounded by f(x), x-axis and the line x=1 and x=2.

Q: Find the area of the region bounded by the graphs of the given equations. y =– x- 3' y = 0, x = 4, x…

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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:

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

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

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Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

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Q: Find the area of the region bounded by the curve y=x^3-3x^2+3 and the x-axis.

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Q: Find the area of the region bounded by f(x) =|x^2−5x+ 6|, the x-axis, and the lines x=1 and x= 4.

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 8x, y = 0

A: Let us plot the region.

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 shaded region  f(x) =8x+2x^2-x^3, g(x) =0

A: f(x) =8x+2x^2-x^3, g(x) =0

Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². 543-2 1…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

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: f (x) = x – 2x – 3

A:

Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

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

A: The functions are f(x)=x2+2  &amp;  g(x)=x-1

Q: Find the area of the shaded region. 18- f(x) = 8x + 2x - x°, g(x) = 0 -4 -18-

A: We have the following equation

Q: Find the area of the region bounded by y = x² - 5x + 6, the x axis, and the vertical lines x = 0 and…

A: Given that y = x2 - 5x + 6 ; y = 0 (x - axis) ; x = 0; x= 4  We have to find the area of the region…

Q: Solve for the area of the region bounded by: x^2 = 4y + 4 and x = y - 2

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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: Find the area of the region enclosed between: f(x)=x^2+3x+16, g(x)=2x^2+x+1.

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Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

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Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

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Q: Find the area of the region bounded by the graphs of y = x2, y= x² – 2r +3 and y= 2x- 1.

A: Given curve is y=x2, y=x2−2x+3 and y=2x-1 we have to find the area of the region bounded by the…

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The exact area of the region bounded by the graphs of y = x² + 2, and the x – axis from r = -1 to x…

A: Given that:

Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

A:

Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

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.