Using rectangles each of whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graphs of the following functions, using first two and then four rectangles. 5. f(x) = x² between x = 0 and x = 1.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Suppose y = f(x) = 5x – x². A graph for this function and area is given below. 23. Shade in the…

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Q: d the area bounded by the graphs of the indicated equations over the given interval (when stated).…

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Q: How many individual areas in the total area bounded by the curve y=x - 3x +2x and by the x-axis from…

A: first we plot the given region then decide how many areas exist

Q: 5. Find the equation of the line x = k that divides the area enclosed by the graphs of x = Vy,x = 3…

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Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: 3 Estimate x dx using right endpoints for n = 4 approximating rectangles. x² dx is approximately

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Q: Find the area between the graph of function and the x-axis over the given interval, if possible.

A: fx=5x-22,  (-∞, 1].

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

Q: 6. Find the area between the curve y = x(x - 3) and the ordinates x = 0 andx = 5.

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

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Q: 1. Find the area bounded between the curves: y = x+1, y = -2x + 7 and x = 0 A. With respect to the X…

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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: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: 2) Find the area of the function f(x)=x² +4 for x=-1 tox=4.

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Q: The area under the graph of f(x) = 3x2 between x = 2 and x = k is 208, where k> 2. Find the value of…

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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: 1 Estimate the area under the graph of f(x) : x2 + 4 over the interval [- 1, 3] using ten…

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Q: 2. Find the equation of the tangent to the functions g(x) = (x −4)² at its y-int. You must use an…

A: Solution:

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: Suppose you estimate the area under the graph of f(x) = x from x = 5 to x = 25 by adding the areas…

A: The given function is fx=x3 from x = 5 to x = 25 Partition type: 20 equal subintervals with right…

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: Use the Midpoint rule with n=4 to approximate the area of the region bounded by the graph of the…

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Q: For the area under the curve f(x) = x(x+1)(x+7) above the x-axis, and between the vertical lines…

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Q: find the total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x“ – 3x + 229, where x…

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Q: Find the area of the region in the xy-plane bounded above by the graph of the function f(x)=9, below…

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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: Suppose that f is a negative function with antiderivative F such that F(1) = 7 and F(3) = 4. What is…

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Q: Find the area between the curve ​f(x)=x^2​+15 and the​ x-axis from x=3 to x=5.

A: Given query is to find the area under the curve.

Q: Find the area between the curve f(x) = x² +12 and the x-axis from x = 3 to x = 6. ...

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

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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: (4) Calculate the area between the two curves of the functions fi(x) = x2 and f2(x) = 2 x + 3

A: Here, the given curves are f1(x)=x2, f2(x)=2x+3 First of all, find the intersection point(s) of the…

Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: For the following graph of a function, estimate the area under the curve on the interval [-6, –1]…

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Q: Find the approximate area under the curve of the given equation by dividing the indicated intervals…

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Q: For the following graph of a function, estimate the area under the curve on the interval [2, 5]…

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Q: A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229 where xx represents…

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Q: For the following graph of a function, estimate the area under the curve on the interval [-2, 6]…

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Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 18: Find the total area of the region between the functior F(x) = x3 – 4x² + 3x and x-axis from…

A: The given curve is we have to find the area bounded by the region f(x)  and x-axis from [-3,3].

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x? – 3x + 229, where x…

A: Given C(X)=0.01x2-3x+229      And R(X)=429-2x Where X is the number of cell phones

Q: Find the exact solution of the function via calculator, then find the numerical solution by using…

A: Given function is fx=2-ex2+x boundaries 0≤x≤1 and h =110       h =0.1   (1) Exact solution:…

Q: 32.g( (z)=z +1, [1, 3,8 rectangles

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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: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

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