1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
babymother [125]
3 years ago
13

Find the average value of the function on the given interval. f(x)=2 ln x; [1,e]

Mathematics
1 answer:
JulijaS [17]3 years ago
8 0

Answer:

f_{avg}=\frac{1}{e-1}

Step-by-step explanation:

We are given that a function

f(x)=2lnx

We have to find the average value of function on the given interval [1,e]

Average value of function on interval [a,b] is given by

\frac{1}{b-a}\int_{a}^{b}f(x)dx

Using the formula

f_{avg}=\frac{1}{e-1}\int_{1}^{e}lnx dx

By Parts integration formula

\int(uv)dx=u\int vdx-\int(\frac{du}{dx}\int vdx)dx

u=ln x and v=dx

Apply by parts integration

f_{avg}=\frac{1}{e-1}([xlnx]^{e}_{1}-\int_{1}^{e}(\frac{1}{x}\times xdx))

f_{avg}=\frac{1}{e-1}(elne-ln1-[x]^{e}_{1})

f_{avg}=\frac{1}{e-1}(e-0-e+1)=\frac{1}{e-1}

By using property lne=1,ln 1=0

f_{avg}=\frac{1}{e-1}

You might be interested in
Please need help explanation need it
nydimaria [60]

Answer:

308 m^3

Step-by-step explanation:

The volume is given by

V = l*w*h  where l is the length , w is the width and h is the height

V = 7*4*11

V = 308 m^3

7 0
2 years ago
1. [-/1 Points]
stiv31 [10]

multiply x times y divide by 6 on both sides and you got your answer

4 0
1 year ago
The diameter of a small grain of sand is about 0.00002 meters, which can be written as 2•10^n
defon

Answer:

N = -5

Step-by-step explanation:

Move the decimal point right until it is right after the first significant figure.

N = 5

But wait! It's a decimal so it has to be negative.

N = -5

6 0
3 years ago
Read 2 more answers
Solve for x: 14-14x^1/3 =2
zmey [24]

Answer: 216/343 or 0.6297

Step-by-step explanation:

14-14x^{1/3} = 2\\14 -2 = 14x^{1/3}\\12 = 14x^{1/3}\\\frac{12}{14} =x^{1/3}\\\frac{6}{7} =x^{1/3}\\(\frac{6}{7})^3 =(x^{1/3})^3\\\frac{6^3}{7^3} =x\\\\\frac{216}{343} = 0.629737609 = x

7 0
3 years ago
After which value of x does function g exceed function f?
uysha [10]
Say this:  "after x=2, g(x) exceeds f(x).   Note that for x=3, g(3) > f(3).  Check that out.
 
3 0
3 years ago
Other questions:
  • Sarah Simpson is insured for bodily injury in the amount of 10/20. She is at fault in an accident in which Fred Vail ns injured.
    11·2 answers
  • Craig has the following set of 13 cards. If a card is randomly chosen from Craig’s set, what is the probability that the card wi
    5·1 answer
  • Diane, Jose, and Bill have a total of $109 in their wallets. Bill has 3 times what Jose has. Diane has $6 less than Jose. How mu
    11·1 answer
  • Multiples of 3 between 81 and 110
    11·1 answer
  • What is the measure of line VN?<br><br> 4.78 <br><br> 2.43<br><br> 4.22
    10·1 answer
  • Given the linear relationship modeled in the table, how much would 5 sandwiches cost ?
    12·1 answer
  • Hitomi has a bag with four chips in it numbered 1 to 4. SHe randomly draws a chip and replaces it three times. What is the proba
    12·2 answers
  • If 39 x 100 =x2 whats 9x199=x3???
    5·1 answer
  • Complete the square.<br> 3x^2-12x=96
    15·2 answers
  • pleaseee fast help me......................prove that the valueof x obtained by sloving 7^x+1/7^x=49*1/49 also satisfy 2^x-2^2=2
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!