Consider the region bounded above by f(x)=−x2+9x+7 and below by g(x)=8x+5. Find the area, in square units, between the two functions over the interval [−1,2]. Do not round, enter an exact answer.

Q: Determine the area, in square units, of the region bounded above by g(x)=−8x+3 and below by…

A: Given g(x)=−8x+3 and f(x)=−7x+16 And the curve g(x) is bounded above and f(x)=−7x+16 is bounded…

Q: Find the area bounded by the line f(x) equals 3X -1, the curve G(x) equals X^2-6X +7 , and the two…

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Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = dx -

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [-1, 2] by…

A: Clearly the given integral can be approximated by the areas of the given triangles.

Q: Find the area, in square units, bounded above by g(x)=6x−1 and below by f(x)=7x−15 over the interval…

A: It is given that region is

Q: Find the area of the region between the curve and the x-axis. In 4 3x f(x) = e - 4 from 0 to 3

A: By using area formula, we calculate the required area of the region.

Q: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

Q: Q2: f(x. y)- x/y over the region in the first quad- rant bounded by the lines y x,y 2x,x 1,x-2

A:

Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

A: The given two curves that bounds a region is,

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: What is the total area between f(x)=−6x and the x-axis over the interval [−4,2]

A: Graph of f(x)=-6x in interval -4 to 2 is shown on board

Q: Determine the area, in square units, of the region bounded above by g(x)=8x+6 and below by…

A: We have to find area between two curves in the interval [-10.15],for more clarification see graph.As…

Q: Find the total area between the curve of the function f(z) = -4z +8 and the z-axis over the interval…

A: I have provided solution in  step2.

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: First, we need to find the points of interesection of f(x)=7x2+3x−45 and g(x)=8x2+22x+45At points of…

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: Determine the area, in square units, bounded above by f(x)=−x2−8x and g(x)=3x+24 and bounded below…

A: Topic = Application of integration

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

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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: 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: 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: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: The given functions are,

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: Consider the region bounded above by f(x)=−2x3−9x2−10 and below by g(x)=−x3−12x2−10. Find the area,…

A: To calculate the area contained between the two given curves (as boundaries)

Q: Solve S using the technique of integration by partial x²-4 fractions A. In B. In +c с. in +c D. A В…

A: Option A

Q: Use substitution to convert the integrals to integrals of rational functions. Then use partial…

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Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

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Q: Find the total area between f(x)=3x2-3 and the x-axis on the interval [-2,2]

A: Calculation:The given curve are f(x) = 3x2 – 3 and the x axis y = 0 on the interval [– 2, 2].The…

Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

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: 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: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

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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: Evaluate f x²+8x+15 dx by using the integration by partial fraction.

A: We will factorize the denominator and then separate hose factors by using partial fraction method.…

Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

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Q: Find the area of the region in the xy-plane bounded above by the graph of the function…

A: Given  fx=711x-2111, x=3 & x=14 To find Area:

Q: Find the area bounded by the function f(x) equals .3x^3-1.5x^2+19 the X axis and the lines X=2 and…

A: We will find out the area under the curve.

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [– 1, 2] by…

A: Given the graph of the function :

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Consider the region bounded by F(x)=10x3 +7x2 -7x +6 and g(x)= 9x3 +8x2 - x +6. Find the area, in…

A: Given query is to find the area bounded by the curves for the given intererval.

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

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Q: The area of the interval lies between z = -2.49 and z= 1.72 is

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Q: Find the area bounded by the two curves f(x) = x2 – 8x + 8 and g(x) = - x² + 6x – 8, and the two…

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 9 -x, and the line perpendicular…

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 between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

A:

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…

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x over the interval 0, 3 by using…

A: The given function f(x)=9-x2 over the interval [0,3]

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.