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) = 60 + 5t (0 st s 5) dollars per day. Find the area between the graphs of R(t) and C(t) for 0st s 5. What does your answer represent? average revenue per day average cost per day average profit per day total revenue for the week total cost for the week total profit for the week

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 bounded by the curves y2 = 4x 4х + у — 6 %3 0

A: We need to find the area bounded by the curves y2=4x4x+y-6=0

Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0

A: Formula: The area between the curves on the interval given by, Given:

Q: Find the area bounded by the following: 1. Curve y²-8y-8x +32= 0 and y²-8y + 4x = 0

A: We will use basic knowledge of integral calculus and the theory of evaluation of integrals.

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

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Q: B- Find the area between the curves: x = y2 and y = x - 2

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: Approximate the area under the curve graphed below from x = 1 to x = 5 using a Left Endpoint…

A: First sub-part. a=1, b=5 and n=4△x=b−an=5−14=44So, △x=1 Now, sketch the graph and determine the left…

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: Approximate the area under the curve graphed below from x = 2 to x = 7 using a Left Endpoint…

A: Let's find.

Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

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: Find the area beneath the curve g(x) = 8x + 3x2 from x = 5 to x = 6

A: Given function is,

Q: Q4. Find the area between curve y = x - 3x + 2 and x-axis from x =0 to x 2

A:

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

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Q: Find the area between the curves x² and 3x – 2

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Q: Find the area between the curve y (2.x + 3)2 and the x-axis, from x = -2 to x = 3.

A:

Q: Find the area between the curve  y = x2 + 3  and the line  y = 2x − 2  (shown below) from x = 0 to…

A: We first sketch the area using a graphing calculator

Q: Find the area contained between the two curves y = 3x - 2² and y=x+x².

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Q: It is possible for the area between two curves to be negative. (T/F)

A: Following are the answers:

Q: 5. Suppose your daily revenue from selling used DUDS Is R(t) = 100 + 10t 0+E5) dollars per day,…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A:

Q: Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

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: Approximate the area under the curve f(x) on the closed interval [1, 3] with 5 circumscribed regular…

A: Given curve f(x)=x2+9x+10 interval 1,3. The objective is to estimate the area under the curve. Area…

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: Find the area between the following curves: y=x^2-30 and y= 10 - 3x

A: To Find the area between the following curves: y=x^2-30 and y= 10 - 3x

Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0 -

A:

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

A:

Q: Find the area between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: 2. Find the area between the curves. x = - 2, x = 1, y = 6x, y = x2 - 7

A: Given: x=-2,x=1,y=6x,y=x2-7

Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

A:

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area between the curves x=63-7y^2 and x=7y^2-63

A: Here two curves are given and we need to find the area between them. The curve equations are shown…

Q: Consider the area of the region bounded by the curves y = 2x - 3x – 9x and y = x - 2x2 - 3x. If A,…

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Q: Approximate the area under the curve of f (x) = x² +3 from 0 to 4 using the Midpoint Rule with n =…

A:

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: The area enclosed between the x-axis and the curve y=x2 between x=1 and x=2 is:

A:

Q: Find the area between the curves x2 and 6x – 5

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Q: Find the area between the curves. y = x2 - 9x + 4 and y = x² + 6 from x = 0 to x = 6

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Q: Find the exact area between the curve f (x) = x³, the x-axis, and x=0 and x=4.

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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: Approximate the area under the curve graphed below from x = 2 to x 6 using a Left Endpoint…

A:

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.