Express the area of the shaded region in terms of an integral (or integrals). Do not evaluate your expression. Choose the correct answer below. Q 11 O A. ((x² - 8) – 7x) đx + x= 11 -1 11 OB. y = 7x -1 11 OC. 11 y=x² -8 OD. S (x- (* -a)) ac

Q: Q.6 Evaluate the integral by interpreting it in terms of area 1) L xdx 2) LV16 - x² dx

A:

Q: dz 2+2vz

A: The given integral,       ∫dz2+2z

Q: Evaluate the indefinite integral. 5 fz¹ √8+zºdz + C

A:

Q: Evaluate the integral. 6. 6 cosh (x) dx X, 4

A: Let x=u Differentiating both sides with respect to 'x', we get ddxx=ddxu12x=dudxdxx=2du

Q: Evaluate the integral by any method. NOTE: Enter the exact answer. x7 dx V4 – 3x16

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. 5x/5 – x² dx; u = 5 – x²…

A: Consider the integral  ∫045x5-x2dx      ; u=5-x2

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ 4x dx/x3 + 4x

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ x dx/x2 - 3x + 2

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Q: Evaluate the indefinite integral by substitution. Method Integral 2(2x+4)5 dx

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Q: Determine ∫2x(x^2 + 5)dx by making a substitution. Then, determine the integral by multiplying out…

A: Evaluate: ∫2xx2+5dx

Q: Evaluate the integrals

A: Given: The integral

Q: indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic…

A:

Q: Find the indefinite integral.

A: Given data: The given expression for the integration is: .   Assume (z-10)=t  and differentiate it…

Q: Evaluate the integral. 0.6 x2 dx V 9 - 25x2

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8. dx : (1 –…

A:

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ dx/x(x + 1)2

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Q: Write a definite integral that represents the area of the shaded region and compute the integral…

A: We have the given curve as y=-x+4 At y=0, we get the value of x as 0=-x+4x=4

Q: Evaluate the integral by any method. NOTE: Enter the exact answer. x7 dx V4 - 3x16

A:

Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: 6x2 – 10x + 2 dx x3 – 3x2 + 2x -SA+B+C A + B + C dx Question: What is A, B, C? And also evaluate the…

A: It can be solved using partial fraction decomposition.

Q: Evaluate the integrals ∫ 1/x6(x5 + 4) dx

A: Integration : ∫1x6(x5+4)dxWe need to perform partial fraction decomposition:

Q: A solid S extends along the x-axis from x = 1to x = 3. For x between 1 and 3, the cross-sectional…

A: Given, x varies 0 to 1 crossectional area =3x2

Q: Find the area bounded by x2 = 4y + 4 and x = y 2. Using vertical element, what is the integral…

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Q: Use the trapezoidal or simpson's rule to approximate the value of the integral from 2 to 3 2/x^2 dx…

A: The value of a definite integral using the trapezoidal rule is given by: Here: Therefore:

Q: .3 2х — 3 -dx 4 x –x

A: First break the given Integral  Then take 4x- x^2 = u and in other one complete the square  Finally…

Q: Express the integral in terms of the variable u, but do not evaluate it. 11x/10 – x2 dx; u = 10 – x²…

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ x3 + 1/x3 - x dx

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Q: Evaluate the integrals ∫3/x dx

A: the given integral is: ∫3xdx we have to evaluate the given integral. let the given integral be I.…

Q: 3 Use only the fact that 3x(4 - x)dx = 22 and the properties of integrals to evaluate the integrals…

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Q: 4) Write a definite integral that represents the area of the shaded region and compute the integral…

A: Given the equation of the line is y=-x+4 Intersection with x-axis: Put y=0 0=-x+4x=4

Q: Evaluate the integrals

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ dt/t4 + 4t2 + 3

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Q: Find the area bounded by y = (11-x)1/2 , the lines 3x = 2 and x = 10, and the X-axis.   (Solve…

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ x dx/x2 + 4x + 3

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Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

Q: Write a definite integral that represents the area of the region. y1 = x2 + 2x + 1 y2 = 2x + 5

A: The given equations of the curves are: y1 = x^2 + 2x + 1 y2 = 2x + 5 At the points of intersection…

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: To evaluate the integral: ∫022x-x3dx Evaluating the integral.…

Q: Use integration by parts to evaluate the integral: (7r + 1)dr

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Q: Evaluate the integral and check your answer by differentiating. ∫ x1/3 (2-x)2 dx

A: we can use integration by parts property Or we can use expand the terms inside the integral. let us…

Q: Evaluate the integral using appropriate substitution ∫(x^2 +1)/(√(x^3 +3x))dx

A: Given an integral: ∫x2+1x3+3xdx Let, x3+3x=t t=x3+3xdt=3x2+3dxdt=3x2+1dxdt3=x2+1dx Substitute value…

Q: the integral using the indicated trigo V-64 dr. x = 8 sec(@)

A: The answer is, C - (8/x), where, C is the constant of integration.   The detailed solution is as…

Q: Evaluate (x + 3) V16 - x2 dx by writing it as a sum of two integrals and interpreting one of those…

A:

Q: Use integration by parts to evaluate the integral. Round your answer to the nearest tenth. In(z) S²…

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Q: Evaluate the integral and check your answer by differentiating.  ∫ [(2/x)+(3sin(x))]dx

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Q: a circular city has a density of population equal to 500/(1+r) where r is the radius, write an…

A: Given: A circular city has a density of population equal to:  5001+r Where r is the radius of the…

Q: Use a change of variables or the table to evaluate the following indefinite integral. 2x2 dx 13-4x

A: Given,          ∫2x23-4x3dx

Q: Evaluate , (x + 3)/4 – x² dx by writing it as a sum of two integrals and interpreting one of those…

A:

Q: 5a) 1 x[In (2x)]3 S.₁- -dx 5b) X ² (x² - 4)" S₁²7 3/2 dx

A: We have to evaluate the given improper integral. Here we will use the following formulas-…

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ 3x2 + 4x + 4/x3 + x dx

A: Assume the given integral be I, Rewrite integral and simplify it…

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.