Suppose your daily revenue from selling used DVDS is R(t) - 100 + 10t (0 sts 5) dollars per day, where t represents days from the beginning of the week, while your daily costs are C(t) - 66 + 5t (0 sts 5) dollars per day. Find the area between the graphs of R(t) and C(t) for 0sts 5.

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: Suppose your daily revenue from selling used DVDS is R(t) = 100 + 10t (0 < t< 5) dollars per day,…

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Q: Find the area of the region enclosed between f(x)=x^2−2x+4 and g(x)=2x^2−3x−2.

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Q: find the area between the graphs of y = (x + 1)* and y 3z +1. a)1, b) 3.

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Q: (d) Find the area between the two curves 3 y = 1+r2 y = r² - 1

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = 2²-² is…

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Q: The area bounded by the curve y = 4x and the lines a = 4 and a = 6 above the a - axis is_ O 208.00…

A: Here we use washer's method to find the area between given curves. The answer is given as follows:

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Consider the function f (æ) = –x² + 9. What is the left rectangular approximation of the area under…

A: Given:       fx=-18x2+9    Interval -6,6 with 6 equal sub intervals.   The left rectangular…

Q: 2. The area between the graphs of a(t) = t2 + 5 and b(t) = 2t3 + 3t? – 4t + 5.

A: According to the guideline we should have been able to solve only one question at a time #2

Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles…

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: 4. Find the area between the parabolas y2 = 4ax and x² = 4ay.

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Q: Find the area of the region bounded by the graph of f(x) = 4 − x2, the x-axis, and the vertical…

A: Given curves: The graph is:

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: Sketch the graph and set up the integral of the area of: a). Inside r1, but outside r2 b). Inside…

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Q: Find the area of the graph of the function f(x, y) + y3/2) that lies over the domain [0, 1] × [0,…

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Q: Q2/ Find the total area between the curve y = -x² – 2x and the X-axis.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: f(x) = 3. 2. 14

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [0, 3] by…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - r, and the line perpendicular…

A: Triangle bounded by the y-axis, the line f(x)=5-(x/7) , and the line perpendicular to f(x) which…

Q: Find the area of a triangle bounded by the y axis, the line f(z) 1 z, and the line perpendicular to…

A: Area of triangle = (1/2)*base*height

Q: Find the area of the region bounded by the graph of f(x) = x3, the x-axis, and the vertical lines x…

A: We first sketch the region using a graphing calculator.

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: Area of the region under the graphs? Integral related question

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Q: Below is the graph of y = x2 +5. 141 12 10 8- 6- 4 2 -3 -2 The area bounded by y = 22 +5 and the…

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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 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 included between the parabolas y² = 4(p+1)(x + p + 1), and y² = 4(p² +…

A: As per the question we are given two parabolas defined as : P1  :  y2 = 4(p+1)(x+p+1) P2  :  y2 =…

Q: What is the area enclosed between the graphs of X1 = y“ and X2 –3y + 4?

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Q: Find the area between the y-axis and the graph X = 127 124 y² 2 1 -3 -2 -1 2 о T 4 3 0 -1 -2 1 on…

A: Given y-axis and x=1y2 on the interval -1,-3

Q: 30. Find the area bounded by the curve 5y²=16x and the curve y²=8x-24. A. 36 B. 25 C. 16 D. 14

A: Topic = Area

Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: Find the area of the region between the graphs of y = 15 – x² and y = - 3x + 5 over the interval 0 <…

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Q: Find the area of the region between the parabola y = 4.x; and the straight 4x – 3y = 4

A: Given curve equation y2=4x,4x-3y=4

Q: Find the area bounded by the curve c²y=x³, the x – axis, and the line x =2c.

A: We find the area bounded by the curve using the integration. Before finding the area, first, we will…

Q: (b) By sketching the graphs, find the area of the region bounded by the parabola and the line, x2 =…

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Q: Calculate the area limited by the graph of the equation r2 = 4sin2∅

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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: Given the graph of the function :

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Q: The area bounded by the curve Y 4x and the lines x 6 and a 14 above the x axis is O 640.00 square…

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Q: For F(x)= 3+3x-2x^2 A. Sketch the graph and the rectangles from x=0 to x=2 using n=4 and right…

A: The given function is:…

Q: Suppose your daily revenue from selling used DVDS is R(t) = 100 + 10t (0 sts 5) dollars per day,…

A: We will use definite integration to find the area.  Area Between the graph of R(t) and C(t) is…

Q: Find the value of c > 0 such that the area of the region bounded by the parabolas x² - c and c2 -x²…

A: Sketch the region and integrate in x variable.

Q: The area under the curve y = 8x bounded by the lines a = 4 and a = 9 above the a – axis is_ 648.00…

A:

Q: Suppose your daily revenue from selling used DVDs is R(t) = 100 + 10t   (0 ≤ t ≤ 5) dollars per…

A: We need to find area between R(t) and C(t) for 0 ≤ t ≤ 5.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

A:

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]

Q: Suppose your daily revenue from selling used DVDS is R(t) = 100 + 10t (0 < t < 5) dollars per day,…

A: R(t)=100+10t    (0≤t≤5)Ct=64+5t        (0≤t≤5)    For finding area in easy way,  a) draw a line x=5…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.