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
TEA [102]
2 years ago
8

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

out the x-axis. (Round your answer to three decimal places.)
Mathematics
1 answer:
Nikitich [7]2 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx

If f(x)=x^2, then

f'(x)=2x

and

b=0\\ \\a=2

Therefore,

SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx

Apply substitution

x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du

Then

SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du

Now

\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))

Hence,

SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}

You might be interested in
I NEED HELP AS SOON AS POSSIBLE
Xelga [282]
The answer is D. 200m = 2cm. That's because to get from meters to centimeters, you need to multiply by 100. 200 * 100 is not 2, therefore D is the answer. 
8 0
3 years ago
Read 2 more answers
A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they double the
valina [46]

Answer:

Boxes sold first week = 104

Boxes sold second week =x+5= 104+5=109

Boxes sold third  week = 109 times 2= 218

Step-by-step explanation:

Let x be the number of boxes sold in first week

the girls sold 5 more boxes the second week

So number of boxes sold in second week is x+5

they double the sales of the second week for the third week

So number of boxes sold in third week is 2 (x+5)

Total boxes sold is 431

x+x+5+2(x+5)=431

x+x+5+2x+10=431

4x+15=431

subtract 15 from both sides

4x=416

divide by 4 on both sides

x=104

Boxes sold first week = 104

Boxes sold second week =x+5= 104+5=109

Boxes sold third  week = 104 times 2= 218

4 0
3 years ago
Simplify the following expression.
Blababa [14]

Answer:

-6x

Step-by-step explanation:

I just answered this

it will equal -6x

good luck :)

5 0
3 years ago
Make up your own problem and solve it
Gennadij [26K]

Answer:

= $ (x + 145 + 145)

= $ (x + 290)

So in this way end of every week her salary will increase by $ 145.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Find the area of the shaded region. Round your answer to the nearest tenth if needed.<br><br> 4B
AlexFokin [52]

Answer:

136.1 inches

Step-by-step explanation:

area of a circle is r^2 x pi

this is 3/4 of a circle

1. so 3/4 x 7.6^2xpi

2. 3/4 x 57.76 x pi

3. .75 x 57.76 x pi

4. 136.1

5 0
3 years ago
Other questions:
  • You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you can represent the measures of
    15·1 answer
  • A tablet sells for $375 at both Kade's Craft Corner and Annie's Art Shack.
    13·1 answer
  • An emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin. Write and solve an equation to find the
    7·2 answers
  • How to find the range when the domain is already given.
    6·1 answer
  • What is 7.2% of 3000
    13·1 answer
  • Mrs. Spencer's class is signing up to play sports. 8/26 of the students want to play soccer and 12/26 want to play basketball. T
    14·1 answer
  • PLZ HELP ME ASAP
    13·1 answer
  • 20 pts !!
    5·2 answers
  • What is the vertex of the equation y = (x - 3)2 + 7?
    11·1 answer
  • The top of Mrs. Vonvilla’s coffee table has the dimensions shown. She wants to put a bumper around the edges of the table to pro
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!