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
Nataly_w [17]
3 years ago
15

How to integrate 1/(1-y)^2

Mathematics
1 answer:
Akimi4 [234]3 years ago
3 0
If you're using the app, try seeing this answer through your browser:  brainly.com/question/866966

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy}\\\\\\ =\mathsf{\displaystyle\int\!\dfrac{-1}{(1-y)^2}\cdot (-1)\,dy}\\\\\\ =\mathsf{\displaystyle- \int\!(1-y)^{-2}\cdot (-1)\,dy\qquad\quad(i)}


Substitution:

\begin{array}{lcl} \mathsf{1-y=u}&\quad\Rightarrow\quad&\mathsf{y=1-u}\\\\ &&\mathsf{dy=-1\,du} \end{array}


So the integral \mathsf{(i)} becomes

=\mathsf{\displaystyle -\int\! u^{-2}\,du}\\\\\\ =\mathsf{-\,\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\ =\mathsf{-\,\dfrac{u^{-1}}{-1}+C}\\\\\\ =\mathsf{u^{-1}+C}\\\\\\ =\mathsf{\dfrac{1}{u}+C}

=\mathsf{\dfrac{1}{1-y}+C}\\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy=\dfrac{1}{1-y}+C} \end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>indefinite integral fraction rational substitution power differential calculus</em>

You might be interested in
Which sum or difference is modeled by the algebra tiles? A. (x2 4x − 2) (x2 − 2x − 4) = 2x2 2x 2 B. (x2 4x − 2) (x2 2x 4) = 2x2
dimulka [17.4K]

Answer:

Because (-x²+2x+3)+(-x²-2x-1) = -x²+2x+3-x²-2x-1 = -2x²+2

Step-by-step explanation:

Hope It Helps!

5 0
2 years ago
HELP REAL QUICK PLS TY
Veronika [31]

Answer:

Step-by-step explanation:

the area is L x W so its 42cm

7 0
3 years ago
Mona had some colored papers. The teacher gave her 12 more papers. she counted all the
timama [110]

Answer:

24

Step-by-step explanation:

really need more information about the subject, but im assuming its just basic addition.

36-12=24

8 0
3 years ago
What is a possible value for the missing term of the geometric sequences?
Ganezh [65]
A(n)=ar^(n-1)  and we can find the rate upon using the ratio of two points...

50/1250=1250r^2/1250r^0

1/25=r^2

r=1/5  so

a(n)=1250(1/5)^1=250

...

You could have also found the geometric mean which is actually quite efficient too...

The geometric mean is equal to the product of a set of elements raised to the 1/n the power where n is the number of multiplicands...in this case:

gm=(1250*50)^(1/2)=250
8 0
3 years ago
Read 2 more answers
(6.) 6x – 4(-2x + 7) + 8 =<br> 8x-19
Fed [463]

Answer:

\frac{1}{6}

Step-by-step explanation:

1. you distrubute the -4 to the -2x and +7.

2.you combine like terms.

3.you get X in one side of the equation.

4.You divide 1 by 6.

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which table could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsi
    12·2 answers
  • A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength
    15·1 answer
  • Please help geometry URGENT
    12·1 answer
  • Simplify the ratio 24/56
    5·2 answers
  • Perform this operation and report the answer to the correct number of significant figures: What is the mass of a cube of aluminu
    15·1 answer
  • Given m||n, find the value of x.
    6·1 answer
  • 1. 2+2=
    8·1 answer
  • Please anyone help!!
    5·2 answers
  • Please help due today!!!!
    8·1 answer
  • Find the equation of the line through (-7, -2) that is perpendicular to the line y = x/3+6.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!