Let f'be differentiable on [0, ) and f (x) > 0 for x > 0. In this project we will compare the area A(x) under the graph of f on [0, x] with the area B(x) of the rectangle with vertices (0, 0), (x, 0), (x, ƒ (x)), and (0, ƒ (x)) (Figure

Q: If RR is the region bounded by the graphs of the functions. f(x)=6x−7.25    and    g(x)=−8x−8.75…

A: Given: f(x)=6x-7.25 g(x)=-8x-8.75

Q: Sketch a continuous function ƒ that is positive over the interval [0, 1) and negative over the…

A: Given that f(x) is posotive over [0,1) and negative over (1,2] And the area bounded by f(x) and…

Q: The area of the region bounded by the curves y =x and y = 20 –x² is drx|-'א-0 'J - »4,4 - S** |20…

A: We will use double integration to find area

Q: integrate the function f over the given region. f(x, y) = 1/lnx  over the region bounded by the…

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Q: The area of the region bounded above by y=3-x, bounded below by VE2-9, bounded from the right by X…

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Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

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Q: Find the area bounded by the curve x = (y+1)2 and y+1 = x2. Show complete solution of points of…

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Q: Find the exact area of the region enclosed by the graphs of x = 8 – y2 and x = 3. You must show on…

A: we have to find the area of the region

Q: (b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curve by rectangles,…

A: Given function is f(x)=1x, for x≠01,   for x=0 Given interval [-1,1] Now we have to divide the…

Q: What is the volume of the solid formed when rotating the region bounded by f (x) = 2/xand the x-axis…

A: Given function is f(x)=2√x

Q: Let f be positive and continuous function for allx≥0. Find the area of the regionenclosed by the…

A: Given problem is : Let f be positive and continuous function for allx≥0. Find the area of the region…

Q: Find the area between the curve f(x) =sinx and g(x) = cosx over the interval x=-2 and x=5

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Q: 4. The area of the region between the curve y=x* and the line y%3D4 is divided into equal partitions…

A: Given curves are y=x2 and y=4.Also given that y=c divided into equal parts of the area.

Q: The region R is bounded by the parabola y = x2 and the line y = 1. Set up definite integrals to find…

A: The equation of parabola is y=x2 and the line is y=1.

Q: compute the area of the surface formed when f(x) = 2 + cosh (x) between 0 and 1 is rotated around…

A: Given problem:- compute the area of the surface formed when f(x) = 2 + cosh(x) between 0 and 1 is…

Q: Use finite approximation to estimate the area under the graph of f(x) = 3x and above the graph of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the area bounded by the curve y = 1+x² and the lines y = 0, x = y and x = 2. Show complete…

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Q: Estimate the area under the graph of f(x) over the interval [- 2, 2] using five approximating a +4…

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Q: area bounded by y= 3, x = 2, y = -3 and x = 0 is revolved about the y-axis

A: Given that y=3, x=2, y=-3 and x=0 Find area

Q: A right circular cone is inscribed in a sphere of radius a. Express the volume v of the cone as a…

A: Given, A right circular cone is inscribed in a sphere. Radius of sphere = a Slant height of the cone…

Q: The area under the graph of the function y = Vsin x from x = 0 to x = 18 is lim i = 1

A: Given: y=sin x   For a function f, above equation can be written as: fx=sin x   To find area under…

Q: Find the volume generated if the area bounded by the curve y=x^2 and the line y=2x+3 is revolved…

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Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

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Q: 24) Using Numerical Integration to estimate area between curve (y=2-x²) and line (y=-x), with n=3

A: We have y=2-x2, y=-x then intersection point is -x=2-x2 ⇒x2-x-2=0 ⇒ x2-2x+x-2=0 ⇒ (x-2)(x+1)=0⇒x=-1,…

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

A: Solution -  Given function is - f(x) = sinxWe have to calculate the area enclosed by f(x) from x =…

Q: Area under the curve y2 = 4x from x=1 to x=4

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Q: Find the of region bounded by the functions f(x) : (В) sin x and g(x) = cos x over the interval [0,…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of…

A: We have, f and g are given as function of x, thus a vertical representative rectangle is convenient…

Q: Find the continuous lest squares approximation of degree 2 for f(x) = cos(xx) on [0,1]. %3D

A: Let P2(x)=a0+a1x+a2x2 is the continuous least square approximation of degree 2 for the function…

Q: What is the area of the region bounded by the curves y=f(x)=x3-4x2+5x and y=g(x)=3x-x2 between x=0…

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Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x)=64-4x^2…

A: Given query is to find the volume of the solid generated.

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

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Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) = 4…

A: NOTE: Refresh your page if you can't see any equations. . here we have first, we need to find the…

Q: 4. Find the area of the region bounded by y = sin x) and y = x² – 8x. Be sure to provide a graph of…

A: The region is bounded by,      y=sinπ8x and y=x2-8x

Q: Use a finite sum to estimate the area under the curve using the midpoint rule f(x)=x^3 on the…

A: Width of the interval [0,2] is = 2-0=2So for two rectangles the width of the subintervals=∆x=22=1So…

Q: Find the area between the curve on the given interval  y= x^3 , y= x^2-1, 1 < x < 3

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Q: f ( - *) de + (a* +) d-

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Q: Line integral f(x,y)ds is equal to a definite integral if C is a smooth curve defined on [a,b] and…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: Use finite approximation to estimate the area under the graph of f(x) = 3x and above the graph of…

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Q: Find the area between the graphs of f(x)=sinx and g(x)=cosx for <x< 4

A: Graph of area from π4to5π4 is shown below÷ Red curve = sin(x) Blue cuve = cos(x)

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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Q: Find the exact area of the region enclosed by the graphs of x = 9 – y and x = 4. You must show on…

A: Given: x=9-y2 and x=4. Let fy=9-y2 and gy=4.   Plot both the equations.

Q: Find an approximation of the area y = 16 - x² over the interval [0,4] using L6 (left end point…

A: Use: Area=∆xf(x1)+f(x2)+f(x3)+f(x4)+f(x5)+f(x6)       where ∆x=b-anwhere n= no. of rectangle…

Q: Find the exact area of the region enclosed by the graphs of x = 9- y2 and x = 7. You must show on…

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Q: Find the area of the region bounded by the graph of f(x) = x sin x and the x-axis between x = 0 and…

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Q: What is the area of the region bounded by the graph of f on [1,3], when f(x)<0 on [1,3] and F is an…

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Q: Find the area under the graph of the function f(x)= 7sin(x) bounded by the x-axis and the lines x=0…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.