Find the area of the region bounded by the graph of f(x)= x(x + 2)(x -3) and the x-axis on the interval [-2,3]. ..... The area is .(Simplify your answer.)

Q: Let A be the area of the region that lies under the graph of f(x) =e -x  between x =0 and x =2

A: The diagrammatic representation of the area is,

Q: Q2/ Find the area of a region bounded by the curve f(x) = 8x' and x-axis and the two lines x=1, x=3.…

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Q: Find the area of the region enclosed by the graphs of f (x) = x3-x2 and g (x) = 2x

A: Given f(x) = x3 - x2   and g(x) = 2x The intersecting points of the functions are,  => x3 - x2 =…

Q: Find area of region f(x)=x2-10x+9 g(x)= -x2+8x+9

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Q: Find the area of the region R bounded by the graph of f and the x-axis on the given interval. Graph…

A: Given - Region bounded by functions To find - Area of the region

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

A:

Q: Find the area (in square units) of the region under the graph of the function f on the interval [0,…

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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: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

Q: Find the total areas of the regions a. Between the graph of f(x) = 1- Vx and the x-axis for 0 < x <…

A: Given:        fx=1-x interval 0≤x≤4  Total area of the region between the curve fx and the x-axis…

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: f (x) = x² + x – 6 - 6

A: By using area bounded by curve formula, we calculate the required area.

Q: Find the area of the region bounded by the graph of f and the x-axis on the given interval.…

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Q: the area of the region under the graph of f on [a, b]. f(x) =  7 x2

A:

Q: Find the area of the region R under the graph of f(x)=e^x/2 from x = 0 to x = 2.

A:

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

A: function f(x)=4-x2 To find area of region bounded by f(x), x-axis and the line x=1 and x=2.

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 bounded by the graph of g(x) = (x − 4)^4 and the x-axis between x = 2…

A: From the given curves

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

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

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Q: Determine the area of the given region. 3. Region between f(x) = x - 4x and g(x) = x.

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

A: Given: The expression to calculate the area under the curve 'y=f(x)' and the x-axis between x=x1…

Q: Find the area (in square units) of the region under the graph of the function f on the interval [-3,…

A: Given the functionf(x)=−x2+9

Q: 5. Find the area of the region bounded by the graphs of f (x) = 2 - x2 and g(x) = x.

A:

Q: Find the area of f(x) = 3 +2x – x² above the x-axis.

A:

Q: Find the area of the region enclosed between f(x)=0.2x^2+10, g(x)=x, x=−7, and x=2.

A: Given curve is: fx=0.2x2+10gx=xx=-7x=2 To find the area of the region enclosed between the curve.

Q: Find the area of the region under the graph of the function f on the interval [0, 10]. f(x) = 10x -…

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Q: f (x) = x – 2x – 3

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Q: The area between the graph of f (x) = x4 and the x-axis over the interval [0, 1]

A: Given equation - f(x) = x4Given intervals = 0, 1Let's draw the curve for the function given -  x…

Q: Find the area of the region between f(x) = x² + 2 and g(x)= x - 1 on the interval [-2,2]

A: The functions are f(x)=x2+2  &amp;  g(x)=x-1

Q: If R is the region between the graphs of the functions f(x) = 4x + 9x2 + 7x – 3 and g(x) over the…

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

A:

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

A: Area Under the Curve Formula     The area under a curve between two points is found out by…

Q: 3. Find the area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x = 1

A:

Q: Find the area of the region bounded by f(x)=-x^2+1, g(x)=2x+4, x=-1, and x=-2.

A:

Q: Find the area of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

A:

Q: Find the area of the region enclosed by f(x) and the x-axis for the given function over the…

A:

Q: 6. Find the area of the region bounded by the graphs of f(x) = 2 - x and g(x) =x.

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

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the area (in square units) of the region under the graph of the function f on the interval…

A: Given fx=9x2-6x-5        1,4

Q: Find the area of the region that lies under the graph of f over the given interval. f(x) = 2 -…

A:

Q: Find the area of the region between the x-axis and the graph of f (x)= x' – 4.x² + 3x, Osxs2. .

A:

Q: Find the area of the region bounded by the graphs of f(x)=5-x^2 and g(x)=x^2-3.

A:

Q: Find the area of the region lying under the graph of f(x) = √4 x from x = 1 to x = 16.

A: It is given that,                 f(x)=4x from x=1 to x=16We have to find the area of the region…

Q: Consider the region, R, bounded above by f(x)=x5^2−6x+9 and g(x)=−3x+27 and bounded below by the…

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Q: Find the area between  F(x) = x^2-5 and the x-axis from x=0 and x=9

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

Q: Find the area of the region bounded by the graphs of the algebraic functions. f(x)=x^2-14x g(x)=0

A: SOLUTION-

Q: 5. Find the area of the region between the graphs of f(x) = x3 – 2x2 + x - 1 and g(x) = -x2 + 3x -…

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Q: Find the area of the region under the graph of the function f on the interval [3, 7]. f(x)=6ex -x

A: To find the area of the region under the given function on the interval [3,7].

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.