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
kozerog [31]
3 years ago
8

Find the area between the graph of the function and the x-axis over the given interval, if possible.

Mathematics
1 answer:
vodomira [7]3 years ago
7 0

Answer:

A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

A = \int_{-\infty}^1 \frac{5}{(x-2)^2}

For this case we can use the following substitution u = x-2 and we have dx = du

A = \int_{a}^b \frac{5}{u^2} du = 5\int_{a}^b u^{-2}du

And if we solve the integral we got:

A= -\frac{5}{u} \Big|_a^b

And we can rewrite the expression again in terms of x and we got:

A = -\frac{5}{x-2} \Big|_{-\infty}^1

And we can solve this using the fundamental theorem of calculus like this:

A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5

So then the integral converges and the area below the curve and the x axis would be 5.

You might be interested in
2(x - 1) – 7x = 18 – 5(x + 4)
iragen [17]
I hope this will help

4 0
3 years ago
The doctor's office where you work needs to store eight filing cabinets with patient information in one of three secure storage
ikadub [295]

Answer:

9 x 7.5

Step-by-step explanation:

Just 9 x 7 = 63 > 55

8 x 5 = 40 < 55

5 x 10 = 50 < 55

Please mark brainliest

8 0
3 years ago
What is 4y when x -3
lord [1]

Answer:

4y-x-3  = 0

Step-by-step explanation:

 Slope = 0.500/2.000 = 0.250

 x-intercept = 3/-1 = -3.00000

 y-intercept = 3/4 = 0.75000

4 0
2 years ago
How many decimeters are in 3.5 dekameters? Use the metric table to help answer the question.
nataly862011 [7]

it’s 350 or B. hope this helps! :)

8 0
3 years ago
The library in Richmond collected $4,170 in overdue fees last year. This year, the library collected $6,672. What is the percent
melamori03 [73]

Answer:

not sure just need points and

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Add. Write fractions in simplest form.<br> 4-12 EVENS
    11·1 answer
  • Any answers? No need for an explanation if you want to sure, the answer would be appreciated!
    6·1 answer
  • By what transformation can the set representing the inverse of a function be found?
    15·1 answer
  • What is -47/10 as a terminating decimal​
    14·1 answer
  • Someone please help me!!!
    11·1 answer
  • HELP ME I NEED YOUR HELP PEALSE will give brainliest
    13·1 answer
  • 8. What is the slope of the line that passes through (4, -15) and (2, -15)?
    12·2 answers
  • Ms. M wants A LOT of tropical fish, so Mr. M must buy the biggest tank. Which tank should he buy, A or B? How much greater is th
    14·1 answer
  • If f(x)=2 sin 3x+C, then the maximum value of f(x) is:<br> 1)C<br> 2) C+2<br> 3) C+3<br> 4) C+6
    12·1 answer
  • What should be your first step when subtracting integers?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!