Suppose your annual income is I(t) = 48,000 + 2,000t (0 sts 3) dollars per year, where t represents the number of years since you began your job, while your annual expenses are E(t) = 41,000 + 1,500t (0 sts 3) dollars per year. Find the area (in dollars) between the graphs of I(t) and E(t) for 0 s t s 3. $ What does your answer represent? your average savings per year O your average expenses per year O your average income per year O the total amount you were able to save over the first three years O the total amount you spent over the first three years the total amount you earned over the first three years

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

A:

Q: 11. Find the area bounded by the curve 5y²-16x and the curve y²=8x-24. A. 30 sq.units C. 16 sq.units…

A: We need to find area bounded by curve.

Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

A:

Q: Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f…

A:

Q: Approximate the area under the t - curve, with degrees of freedom 29, to the right of t = 2.462…

A: The degrees of freedom is 29.

Q: Below is the graph of y = x +5. 20- 15 10- -4 -3 -2 -1 0 1 The area bounded by y = x +5 and the…

A: Given problem:- Find The area bounded by y= x2 +5 and the x-axis from  x=-3 to x = -1

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…

A:

Q: Find the area between the graph of y and the r-axis for a E [0, b] where b is a (2x2 + 1)2 positive…

A:

Q: Find the area between the graph of y = x - 6x + 8 and the x-axis from x = 1 to x = 3.

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Q: Find the total area between the graph of f(x)=x2−5 and the​ x-axis from x=0 to x=6.

A:

Q: what is the decimal value for the right-hand sum of the area under the curve f(t)=t^2 from t=0 to…

A: Solution

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

A: Given: Revenue function is Rt=100+10t for 0≤t≤5. Cost function is Ct=66+5t for 0≤t≤5.   Setup the…

Q: 1200 1100 1000 900 800 700 600 500 400 300 200 100 100 Find the (exact) area under the curve y = 4x*…

A:

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: Below is the graph of y = x² +5. 401 D 30- 20 10- -3 -2 -1 0 1 2 3 4 5 6 The area bounded by y = x²…

A: the area bounded by the curve y=x^2 +5 and the x axis from x=2 to x=5

Q: For the area enclosed between the curves of the equation f (x) = x and g (x) = k to be 30 (ul), a…

A: here we have to find the intersection points compare both functions  so upper and lower limit…

Q: "In Computing the area between two curves, why does f(x) have to be greater than g(x) over the…

A: In computing the area between two curves, why does f(x) have to be greater than g(x) over the…

Q: O 1hr36mins X Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval…

A:

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: Suppose your annual income is I(t) = 48,000 + 2,000t (0 sts 3) dollars per year, where t represents…

A: According to guidelines we should have been able to solve only first question at a time # first

Q: Below is the graph of y = x² +5. 141 12 10- 8 6- 4 2- -3 -2 -1 2 The area bounded by y = 22 +5 and…

A:

Q: 3. Find the area bounded by the curve ay² = r8 and the line * = 4 a. Ans. 142 a².

A: Find the area bounded by the curve.

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…

A:

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

A: To find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

A:

Q: The area between the curves f(x)= x^2,and g(x)=1 1/2 1/4 O 4/3 O 1/3

A:

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: c) [ 1: Estimate the area under the graph of f(x) = x² - 1 from x = 1 to x = 3 using four…

A:

Q: Draw the graphs and find the area between the curves f (x) = x - x+3 and g(x) = -4x+1.

A: Let's find.

Q: Draw the graphs and find the between the area curves f(x) = (-1)*x² +(-1)°(c+3)x+(-1)*(a+2) and…

A:

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

A:

Q: The area enclosed by the two curves y = x² - 4 and y = x - 4 is given by. a. f(x-x²) dx b. (x²-x) dx…

A:

Q: Sketch the graphs of the functions. (x) = Vx and g(x) - x² 10 10 -10 5. 10 -10 10 10 -1아 y 10 -10 10…

A: To find the area enclosed by the graphs fx=xgx=x2

Q: Calculate the surface area of revolution of f(x) = 3√(x) + 2 about the y-axis in [2,8]. Graph.

A: Given data:   The expression for the given function is: f(x)=x1/3+2.   The expression for the given…

Q: B) Find the area between the parabolas x = y² - 1 and x = 2y² - 2

A: Topic = Area

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

A:

Q: The total area bounded by the graph of y =r 2. 1 and the x-axis is represented by

A:

Q: A The rates at which rain fell, in inches per hour, in two different locations t hours after the…

A: Given:-f(t)=0.73t3-2t2+t+0.6g(t)=0.17t2-0.5t+1.10≤t≤2To find: area between the graph of f(x) and…

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A:

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: The area enclosed between the curves p(x) = + *+ 3 and g(*) = O 16 is 18 49 O -49 O 9 36 O -16 O -36…

A: To find the area enclosed between the curves.

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

A:

Q: The positive number c for which the curve yd- divides the area under the curve y 2209- from O to 47…

A: Given

Q: Calculate the area between the graph of f(x) = x² (x + 4) and the x-axis given x E [0, 5].

A:

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

A:

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.