Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = x3 - 1 on [-1, 2]

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: Find area under the curve of this integral?

A:

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 enclosed between these graphs and the vertical lines x=3 and x=4.…

A: Here we used area between the two curves

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 R bounded by the graph of f and the x-axis on the given interval. Graph…

A: Given - Region bounded by functions To find - Area of the region

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

A:

Q: Find the area of the region under the graph of the function f on the interval [4, 11]. f(x) = 2x - 2…

A: use integral to evaluate the are bounded by curve over the interval

Q: Find the area of the region under the graph of the function f on the interval [5, 11]. f(x) = 4x - 6…

A:

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

A: We have to find the area

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…

A:

Q: Find the area enclosed between f(x) = 0.3x² + 4 and g(x) = x from x = -3 to x = 4.

A:

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

A:

Q: Find the area of the region between the graphs of f(x) = 3x + 8 and g(x) = x2 +2x +2 over [0, 2]…

A: according to graph area of shaded region can be written as given below A=∫02fx-gxdx

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

A:

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. f(x)…

A: Given. Y = e-3x Area is  dA = e-3xdx Interval is  X>=8

Q: Find the area of the region bounded by f(x) = x2 and g(x) = x3 on [−2,4]

A:

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

A:

Q: Find the area of the region under the graph of f(x)=2x2−4x+2 on [−2,3].

A: The area can be calculated using the concept of definite integral.

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

A: Given f(x)=-3x3+3x2+24x-4 and g(x)=-4x3-10x2-6x-4

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  &  g(x)=x-1

Q: Find the area of the region that is completely bounded by the two curves f(x) = – x² – 3x + 19 an…

A:

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x2 – 8x + 20; [-1, 2]

A:

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

A:

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

A:

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.

A:

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

A:

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

A:

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

A:

Q: Find the area A of the bounded region between the grapghs of f(x) = 2x^2+x-1 and g(x)=x^2+3x+2.

A: Given equation of the graph are as follows.

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

A:

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

A:

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: Determine the area, in square units, of the region bounded by f(x)=−x2+21x−44 and g(x)=5x+19 over…

A: Determine the area, in square units, of the region bounded by f(x)=−x2+21x−44 and g(x)=5x+19 over…

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 between f(x) = x - 1 and g(x) = -x² + 6x - 5 %3D

A: We have been given the graphs f(x)=x-1g(x)=-x2+6x-5

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. 1…

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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-

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.