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
Llana [10]
3 years ago
8

Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis.

Mathematics
1 answer:
aivan3 [116]3 years ago
3 0

Answer:

0.089

Step-by-step explanation:

f(x) = -ln(x) and g(x) = x²

Start by graphing the region.  The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right.  The region is the triangular area between the curves and above the x-axis.

If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section.  The thickness of this square is dy.  So the volume of the square is:

dV = A dy

dV = s² dy

dV = (x₂ − x₁)² dy

dV = (e⁻ʸ − √y)² dy

The total volume is the sum of all the squares from y=0 to y=0.426.

V = ∫ dV

V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy

Evaluate with a calculator:

V ≈ 0.089

You might be interested in
NEED ANSWER FAST PLASE FAST
Dovator [93]

Answer:

D. no solution

Step-by-step explanation:

h-z=3(1)

h=3+z(minus z from both side)

put in the second equation

-3h,+3z=6(2)

-3(3+z)+3z=6

-9-3z+3z=6

-9=6( not true)

so the equation doesn't have a solution.

3 0
2 years ago
I need solve this problem can you help me please ?
VARVARA [1.3K]
ED = 68
Angle GKH = 31
ABD = 224
Angle AKB = 112
5 0
3 years ago
Adrian spends $238 on a DVD. If he buys 18 DVD,s approximately how much money will he spend in all?​
bija089 [108]

Answer:

Adrian would spend exactly $4,284.

Step-by-step explanation:

Multiply the cost by the number of products purchased:

$238 x 18 = $4,284

Have a good day :)

7 0
3 years ago
Read 2 more answers
What is the interest rate $14,095 at 3.8% for 5 1/2 years
ivanzaharov [21]

Answer:

373737373746372838484883848r

7 0
2 years ago
What is 1/4 - 1/3 + 1/3=​
mamaluj [8]

Answer:

1/4

-1/3+1/3 cancels each other

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • At a local store you find the following prices listed: Cellophane tape 2 rolls for $1.28 Note pads 3 pads for .87 Highlighters 1
    14·1 answer
  • Please help me :( thank you :( very grateful if you answer :0 pic down below
    6·1 answer
  • How many boxes are shipped
    12·2 answers
  • What is the answer to 5x +3 &lt; 18
    9·1 answer
  • 3/2 x 3 x 1/5 please help me
    12·1 answer
  • (3/2)x - -4 =13 what is x?
    10·1 answer
  • Simplify each expression as much as possible, and rationalize denominators when applicable. √(17/25)=?
    8·1 answer
  • What’s the total badges and buy all the Boy Scouts<br> 26<br> 25<br> 52<br> 78
    13·1 answer
  • 74tens=how many hundreds
    5·1 answer
  • One number is three less than eight times another number. If the sum of the numbers is 69, find the numbers.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!