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
elena-14-01-66 [18.8K]
2 years ago
5

chegg evaluate the following integral using trigonometric substitution. dx/square root(x^2-81), x > 9

Mathematics
1 answer:
vesna_86 [32]2 years ago
6 0

Integration will be ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c  .

Given  ∫ 1 dx / ( x^{2} - 81 )

Put ,

x = 9 secθ

dx = 9 secθ tanθ dθ

and

\sqrt{x^{2}  - 9^{2} } = 9 tanθ

Substituting values in  ∫ 1 dx / ( x^{2} - 81 ) ,

∫ (9 secθ tanθ ) dθ / ( 9 tanθ )

∫ secθ dθ = ln | secθ + tanθ | + c

                = ln | ( x /9 ) + ( \sqrt{x^{2}  - 9^{2} } / 9 ) | + c

              = ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c

Hence , the integration will be ln | ( x /9 ) + ( \sqrt{(x/9)^{2} - 1 } ) | + c .

To learn more on integration follow link :

brainly.com/question/20156869

#SPJ4

You might be interested in
Deshaun started baking at 9:25 AM and finished at 10:41 AM How long did it take him? Give your answer in hours and minutes​
Zepler [3.9K]

Answer:

1 hour and 16 minutes

Step-by-step explanation:

you just have to count up from 9:25 to 10:41 and translate the amount of minutes you counted into hours

7 0
2 years ago
Roy has bought two square photo frames. The ratio of their sides is 4:1. If PQ = 12 inches, what is AB? A. 12 in. B. 9 in. C. 6
aleksklad [387]

Answer:

D. 3

Step-by-step explanation:

If the ratio of their sides is 4:1, and if PQ=12 inches, then Ab=12/4=3 inches.

6 0
3 years ago
Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
Explanation

We must the tangent line at x = 3 of the function:

f(x)=(\ln x)^3.

The tangent line is given by:

y=m*(x-h)+k.

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

2) By evaluating the result of f'(x) at x = h = 3, we get:

m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.

3) The value of k is:

k=f(3)=(\ln3)^3

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

y=(\ln3)^2*(x-3)+(\ln3)^3.

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

6 0
1 year ago
The sale price of a scooter s $850. The original price was first discounted by 25% and then discounted an additional 15%. What w
ira [324]

Answer:

$1,190

Step-by-step explanation:

$850(0.25) = 212.50

$850(0.15) = 127.50

$850+212.50= 1,062.50

1,062.50+127.50= 1,190

5 0
3 years ago
Can someone please help me on 12
mixer [17]
Well first, you need to solve within the parentheses. You would get 23.8 - 14 - 8.6

Then you would subtract them in order, and your answer would be 1.2
6 0
3 years ago
Other questions:
  • What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12?
    15·1 answer
  • If Y equals -2X -9 what is the value of Y when X equals -11
    7·1 answer
  • A juggler has a bag containing four yellow balls, five green balls, four blue balls, and one red ball, all the same size. The ju
    12·1 answer
  • Write a prime factorization of each of the numbers below
    8·1 answer
  • Researchers in education are performing a study to see if listening to soothing music while taking a standardized math test incr
    12·1 answer
  • a number is divided into 2 parts. one part is 10 more than the other, 2parts are in the ratio 5:3 find the number n the 2 parts​
    10·1 answer
  • Whiw do you graph y=3x-2
    7·1 answer
  • The angle measurements in the diagram are represented by the following expressions.
    15·2 answers
  • What is 39,800,000 in scientific notation? A. 3.98 x 10 B. 398 x 10 C. 3.98 x 10 D. 39.8 x 10
    7·2 answers
  • Divide x - 3x² - 10x+ 24 by X-2<br> Step 1 - Fill in the missing number:<br> k | 1 -3 -10 24<br> k =
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!