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Dima020 [189]
3 years ago
11

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.

) ∫4x2 lnx dx ; u= lnx , dv=4x 2dx
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
5 0

Take

u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x

\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3

Then

\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C

=\boxed{\dfrac49x^3(3\ln x-1)+C}

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Find the distance between (1,0) and (9, 15).<br> Distance =
Mnenie [13.5K]

Answer:

d = 17

Step-by-step explanation:

d = √ (9 − 1) 2 + (15− 0)^2

d = √ (8) ^2 + (15) ^2

d = √ 64 + 225

d = √289

d = 17

6 0
3 years ago
Which of the following is a common characteristic of a binomial distribution?
Tanya [424]

Answer:

E. Each trial is independent

Step-by-step explanation:

I'm not completely sure why all binomial distribution trials are independent, but there are requirements for binomial distributions.

These requirements are:

- Each outcome is either a success (p) or a failure (Q)

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2 years ago
Evaluate g(n-7) if g(x) =x^2-5 / 3x
aleksandrvk [35]

Answer:

g(n-7)=\frac{n^2-14n+44}{3n-21}

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g(x)=\frac{x^2-5}{3x}

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g(n-7)=\frac{(n-7)^2-5}{3(n-7)}

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7 0
3 years ago
Carlos is 33 years younger than Kristen. 2 years ago, Kristen's age was 2 times Carlos's age. How old is Carlos now?
ale4655 [162]

Answer:

Carlos is 35 years old now

Step-by-step explanation:

Assume that Carlos is x years old now

∵ Carlos is x years old now

∵ Carlos is 33 years younger than Kristen

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∴ Kirsten is x + 33 years old now

2 years ago

∵ Carlos's age = x - 2

∵ Kristen's age = x + 33 - 2 = x + 31

∵ Kristen's age was 2 times Carlos's age

- Equate Kristen's age by 2 times Carlos's age

∴ x + 31 = 2(x - 2)

- Simplify the right hand side

∴ x + 31 = 2x - 4

- Subtract x from both sides

∴ 31 = x - 4

- Add 4 to both sides

∴ 35 = x

∵ x represents Carlos's age now

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3 years ago
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