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
Kipish [7]
3 years ago
13

Integralplease help me

Mathematics
1 answer:
scoundrel [369]3 years ago
4 0
Recall that the product rule for derivatives tells us that, for two functions f=f(x) and g=g(x),

\dfrac{\mathrm d}{\mathrm dx}[fg]=\dfrac{\mathrm df}{\mathrm dx}g+f\dfrac{\mathrm dg}{\mathrm dx}

Integrating both sides with respect to x gives the reverse "rule" for integration:

\displaystyle\int\frac{\mathrm d}{\mathrm dx}[fg]\,\mathrm dx=\int\frac{\mathrm df}{\mathrm dx}g\,\mathrm dx+\int f\dfrac{\mathrm dg}{\mathrm dx}\,\mathrm dx
\implies \displaystyle\int f\frac{\mathrm dg}{\mathrm dx}\,\mathrm dx=fg-\int\dfrac{\mathrm df}{\mathrm dx}g\,\mathrm dx

You might know this process by the name "integration by parts". This is the standard method for the given integral.

Take

f=x\implies\dfrac{\mathrm df}{\mathrm dx}=1
\dfrac{\mathrm dg}{\mathrm dx}=e^{-2x}\implies g=-\dfrac12e^{-2x}

and so

\displaystyle\int xe^{-2x}\,\mathrm dx=-\dfrac x2e^{-2x}+\dfrac12\int e^{-2x}\,\mathrm dx

The remaining integral is trivial, and the overall result is

\displaystyle\int xe^{-2x}\,\mathrm dx=-\dfrac x2e^{-2x}-\dfrac14e^{-2x}+C
You might be interested in
The figure shows the relationship between the number of miles per gallon on the highway and that in the city for some cars.
Leno4ka [110]

In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:

For each additional city mpg, the highway value goes up by

0.9478 mpg.

And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

According to the statement

we have given that the relationship between the number of miles per gallon on the highway in the graphical representation and that in the city for some cars.

And we have to give some reasons for the given statements.

So, For this purpose, we know that the

A. In this statement we have to tell that the what is shown in the given relationship in the graph.

So, For each additional city mpg, the highway value goes up by

0.9478 mpg.

And the second statement is

B. I this we have to tell the intercept of the plane in the given Relationship.

So, It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

So, In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:

For each additional city mpg, the highway value goes up by

0.9478 mpg.

And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

Learn more about graph here

brainly.com/question/4025726

Disclaimer: This question was incomplete. Pleas find the full content below.

Question:

The figure shows the relationship between the number of miles per gallon on the highway and that in the city for some cars.

a. Report the slope and explain what it means.

b. Either interpret the intercept​ (7.792) or explain why it is not appropriate to interpret the intercept.

#SPJ4

8 0
2 years ago
Factor 6(×)^3+43(×)^2+79(×)+12
Marysya12 [62]
The answer is (6x+1)•(x+4)•(x+3)
3 0
3 years ago
The length of s is 2/3 the length of t. If s has an area of 368 cm squared find the perimeter of the figure
ser-zykov [4K]
s = \frac{2}{3}t
\\\ \frac{2}{3}t*t = \frac{2}{3}t^2
\\\ \frac{2}{3}t^2 = 368
\\\ t^2 = \frac {3}{2}368
\\\ t^2 = 552
\\\ t \approx 23.5
\\\ s \approx 15.6
\\\ P \approx 78.2
3 0
3 years ago
Read 2 more answers
PLEASE ANSWER ASAP!!!!!!!!!!!!!
Licemer1 [7]

Answer:

Since you have to distribute the 4 to both terms in parentheses, the equation is simplified like this:

1 + 12x - 40 -12x

= 1 - 40

= -39

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A) In 2000, the population of a country was approximately 5.82 million and by 2040 it is projected to grow to 9 million. Use the
mezya [45]

Answer:

By 2086

Step-by-step explanation:

The provided equation is:

A=A0*e^{k*t} , where:

A=total of population after t years

A0=initial population

k= rate of growth

t= time in years

Given information:

The final population will be 15 million, then A=15.

We start in 2000 with a 5.82 million population, then A0=5.82.

Missing information:

Although k is not given, we can calculate k by using the following statement, from 2000 to 2040 (within 40 years) population is proyected to grow to 9 million, which means a passage from 5.8 to 9 million (3.2 million increament).

Then we can use the same expression to calculate k:

A=A0*e^{k*t}

9=5.8*e^{40*k}

ln(9/5.8)/40=k

0.010984166494596147=k

0.011=k

Now that we have k=0.011, we can find the time (t) by which population will be 15 million:

A=A0*e^{k*t}

15=5.8*e^{0.011t}

ln(15/5.8)/0.011=t

86.38111668634878=t

86.38=t

Because the starting year is 2000, and we need 86.38 years for increasing the population from 5.8 to 15 million, then by 2086 the population will be 15 million.

4 0
3 years ago
Other questions:
  • If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
    8·2 answers
  • Use properties of addition and subtraction to evaluate the expression. −24−8−26 Enter your answer in the comments below.
    15·1 answer
  • Approximate √52 to the tenths place
    15·2 answers
  • What is the equation, in point slope form, that goes through (-8, 1) and has a slope of 5/6
    15·1 answer
  • Someone help me please
    7·1 answer
  • Two friends shop for fresh fruit. Jackson buys a watermelon for ​$8.85 and 3 pounds of cherries. Tim buys a pineapple for ​$3.35
    14·1 answer
  • What is the potential energy of a 500-N pole-vaulter when she is 4 m above the ground?
    8·1 answer
  • Plz help, And no links please
    9·1 answer
  • Which expression can be used to represent the phrase “four less than seven”?
    5·2 answers
  • Tyrell worked part-time last summer. He worked for 6 weeks and earned
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!