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meriva
3 years ago
6

This question is designed to be answered without a calculator. Use the antiderivative formula shown, where f(u) represents a fun

ction. Integral of (l n u) d u = u ln u – f(u) + C Which function represents f(u)?
Mathematics
1 answer:
Phoenix [80]3 years ago
8 0

Answer:

f(u) = u

Step-by-step explanation:

Given

\int {\ln(u)} \, du = u[\ln(u) - f(u)] + c

Required

Find f(u)

To do this, we start by integrating the left-hand side

\int {\ln(u)} \, du = u\ln(u) - f(u)+ c

Using integration by parts, we have:

\int {fg'}  = fg - \int f'g

So, we have:

f = \ln(u)

Differentiate

f'=\frac{1}{u}

g' = 1

Integrate

g=u

So:

\int {fg'}  = fg - \int f'g

\int \ln(u)\ du = \ln(u) * u - \int \frac{1}{u} * u\ du

\int \ln(u)\ du = u\ln(u)  - \int \ du

So, we have:

u\ln(u)  - \int \ du = u\ln(u) - f(u) + c

Integrate du using constant rule

u\ln(u)  - u + c = u\ln(u) - f(u) + c

Subtract c from both sides

u\ln(u)  - u = u\ln(u) - f(u)

Subtract u ln(u) from both sides

- u =  - f(u)

Rewrite as:

f(u) = u

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This recipe makes 6 portions of chocolate mousse.
trasher [3.6K]

Answer:

Chocolate - 420g

Eggs - 27

Lemon juice - 85ml

Sugar - 140g

Step-by-step explanation:

Given that:

Initial amount of ingredients:

Chocolate - 600g

Eggs - 36

Lemon juice - 100ml

Sugar - 200g

Amount of ingredients used :

Chocolate - 180g

Eggs - 9

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Amount of ingredient left :

Initial amount - Amount used :

Chocolate : 600g - 180g = 420g

Eggs : 36 - 9 = 27

Lemon juice : 100ml - 15ml = 85ml

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4 0
3 years ago
X- 12 = 5x2 in standard form
Rudik [331]

Answer:

It is: -5x^2 + x - 12 = 0

Step-by-step explanation:

4 0
3 years ago
What is the median of the data below?<br><br> 45, 19, 23, 67, 28, 35, 46, 21, 58, 60, 23, 51
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To find the median, you will need to list the data from least to greatest and find the middle number.

19, 21, 23, 23, 28, 35, 45, 46, 51, 58, 60, 67

Cross out a number on both sides until you reach the middle number. In this case, we are left with 2 numbers that are in the middle since there is an even amount of numbers. 

When you reach the time where you have two middle numbers, we have to find the average of those two numbers. Our two middle numbers are 35 and 45. Since we have to find the average of those two numbers, we can add them. (35 + 45 = 80). Now, since we have two middle numbers, we have to divide them by 2. 
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Answer: \fbox {Median = 40}
4 0
3 years ago
Read 2 more answers
Write the given trinomial if possible as a square of a binomial or as an expression opposite to a square of a binomial:
Ksenya-84 [330]

\frac{4}{9}b^2 + 0.4bc + 0.09c^2 = \frac{4}{9}b^2 + \frac{4}{10}bc  + \frac{9}{100}c^2 = (\frac{2}{3}b + \frac{3}{10}c)^2

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3 years ago
Which is the solution to the system of equations? y=−3/2x−11/2; 6x+y=−4
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Answer:

x= 1/3  and y=−6

Step-by-step explanation:

If you want step by step explanation you can get your explanation from

https://www.mathpapa.com And just type that answer in where it says what do you want to  calculate? type it in that box and it give you step by step but i gave you the answer up top you just need the explanation the explanation is hard to type in here that's why i have you that website :)

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