Determine the area, in square units, of the region bounded by f(x)=10x3+x2−21x−9 and g(x)=9x3+x2−5x−9 over the interval [2,6].

Q: Find the area of the region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

Q: determine the area in square units, of region bounded by f(x)=-5x^3-3x^2-7x+4 and…

A:

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: 3. Find the area of the region bounded by y = x², y = 8 - x² and y = 4x + 12.

A:

Q: Sketch the region bounded by the graphs of the equations f(x) = x2 + 2x, g(x) = x + 2 and find the…

A: The region bounded by the graph is as below

Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3

A: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3.

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: The region between the graphs of y = x² and y = 3x is rotated around the line x = 3.

A: Given data:   The expression first curve is: y=x2. The expression for the second curve is: y=3x. The…

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

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

A:

Q: Find the geometric area of the region bounded between the graphs of f (x), g(x) as given: f(x) = x2…

A: Sketch the graphs as shown below.

Q: Find the area of the region bounded by y = x^2 - 5x + 6, the x-axis, and the vertical lines x = O…

A: here we have .............the x-axis .............upper and lower limit (2 vertical lines)

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

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: 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 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: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: Find the area bounded by the line f(x)=2x+2, the curve G(x)=X^2-6X +9 and the two vertical lines X=1…

A: Given:       fx=2x+2        gx=x2-6x+9        x=1,x=5 Area bounded by line and curve is:…

Q: Approximate the area under the curve f(x) on the closed interval [1, 3] with 5 circumscribed regular…

A: Given curve f(x)=x2+9x+10 interval 1,3. The objective is to estimate the area under the curve. Area…

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

A:

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x2 – 6x + 14; [-1, 2]

A: Given  function is  : f(x) = x2 - 6x + 14  ; [ -1, 2 ] Method to find area under the curve : The…

Q: Find the area of the region bounded by the lines ( y=x2 ) & (y=2+x) for xs 0.

A:

Q: Find the area of the region enclosed by the curve y=x²-3x³ + 2x² at interval from x=0 to x = 2.…

A: The graph of the curve y=x4-3x3+2x2 is To evaluate: The area of the region enclosed by the given…

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 by the graphs of y2=1-x and 2y= x+2.

A:

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

A:

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 the curve and the​ x-axis. ​f(x)=36−x2​, from −8 to 8.

A: The function is given by fx = 36-x2;  -8≤x≤8 To evaluate : The area of the region between the curve…

Q: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

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

A:

Q: Find the area of the region enclosed by the curves f(x) = 7x + 1 and g(x) = 5x + 17, and the lines x…

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 (in square units) of the region under the graph of the function fon the interval [-1,…

A:

Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

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 bounded by f(x)=-x^2+1, g(x)=2x+4, x=-1, and x=-2.

A:

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 between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

A:

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 value of k between –1 and 2 such that the area of the region bounded by the lines y = -x, y…

A: we know that the area of a triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by…

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…

A:

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…

A:

Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…

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.