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weeeeeb [17]
3 years ago
9

For which of the following integrands will the table method for parts produce an antiderivative?

Mathematics
1 answer:
Sonja [21]3 years ago
8 0

Answer:

x³ sin(x)

Step-by-step explanation:

Tabular method is a special form of integration by parts.  It works by taking derivatives of u and integrals of dv.  You multiply diagonally, then sum the results, alternating the signs.

The important thing to note is that this will produce an antiderivative only if the derivatives of u eventually become 0.  So the correct choice is x³ sin(x), because the derivatives of x³ eventually becomes 0:

d/dx (x³) = 3x²

d/dx (3x²) = 6x

d/dx (6x) = 6

d/dx (6) = 0

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ivolga24 [154]

Answer:

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Step-by-step explanation:

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About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil
Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

nCx=\frac{n!}{x!(n-x)!}

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}

P(1,2,0.16)=0.2688

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0.0256 + 0.2688 = 0.2944

7 0
3 years ago
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madreJ [45]

Answer:

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Step-by-step explanation:

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3 0
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