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
kakasveta [241]
4 years ago
9

Integral of 1/sqrt (81-225x^2)

Mathematics
1 answer:
ehidna [41]4 years ago
8 0
\displaystyle\int\frac{\mathrm dx}{\sqrt{81-225x^2}}

Let x=\dfrac9{15}\sin t, so that \mathrm dx=\dfrac9{15}\cos t\,\mathrm dt and the integral becomes

\displaystyle\int\frac{\dfrac9{15}\cos t}{\sqrt{81-225\left(\frac9{15}\sin t\right)^2}}\,\mathrm dt
\displaystyle\int\frac{\dfrac9{15}\cos t}{\sqrt{81-225\times\frac{81}{225}\sin^2 t}}\,\mathrm dt
\displaystyle\frac1{15}\int\frac{\cos t}{\sqrt{1-\sin^2 t}}\,\mathrm dt
\displaystyle\frac1{15}\int\frac{\cos t}{\sqrt{\cos^2 t}}\,\mathrm dt
\displaystyle\frac1{15}\int\frac{\cos t}{|\cos t|}\,\mathrm dt

When \cos t>0, you have |\cos t|=\cos t. Under these conditions, you can write

\displaystyle\frac1{15}\int\frac{\cos t}{\cos t}\,\mathrm dt=\frac1{15}\int\mathrm dt=\frac t{15}+C

and back-substituting yields

\dfrac{\arcsin\frac{15x}9}{15}+C=\dfrac{\arcsin\frac{5x}3}{15}+C
You might be interested in
If g(x) = -5x + 13, find g(-1)
givi [52]

To solve this problem, we must substitute the value of -1 in for x in the function. This means that for every x there is in the equation, we must substitute the value -1 in for it in order to find the value of g(-1). This is modeled below:

g(x) = -5x + 13

g(-1) = -5(-1) + 13

Next, we must simplify using the order of operations. PEMDAS outlines this concept, telling us to simplify parentheses first, exponents next, then multiplication and division, and finally addition and subtraction. In this case, we will solve the multiplication and then the addition, as modeled below:

g(-1) = -5(-1) + 13

g(-1) = 5 + 13

g(-1) = 18

Therefore, your answer is 18.

Hope this helps!

5 0
3 years ago
Using the digits 1-7 to create a 7 digit number that can be rounded to 6,300,000
otez555 [7]
6,317,927 can be a 7 digit number that rounds to 6,300,000.

Hope this helps.
5 0
3 years ago
(ii) A retailer paid Rs 40000 for an article after receiving a discount of 20% the marked price from the manufacturer. He sold t
Triss [41]

Answer:

the answer is C

Step-by-step explanation:

40,000/.80 = 50,000

50,000 x .10 = 5,000

50,000 - 5,000 = 45,000

45,000 x .06 =2700

45,000 + 2,700 = 47,700

6 0
2 years ago
3
Schach [20]

Already answered here: brainly.com/question/26807124

8 0
3 years ago
24.9+(-51.7)= what’s the answer for this question?
Molodets [167]

Answer:−26.8

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Three ways to get one and one third
    11·2 answers
  • What do you think about geometry?
    9·1 answer
  • The roots of the equation 3x^2-4x+2=0​
    5·1 answer
  • Lin has a scale model of a modern train. The model is created at a scale of 1 to 48
    5·1 answer
  • Given the polygon containing Point P.
    15·2 answers
  • Solve :1/1-x^a-b +1/1-x^b-a​
    12·1 answer
  • You are 420 miles from home and you are driving toward home at an average rate of 60 miles per hour. The distance d (in miles) a
    8·1 answer
  • What is the missing value:<br><br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B1%7D" id="TexFormula1" title="\frac{16}{1
    6·2 answers
  • Write in slope-intercept form x+y=-15
    6·1 answer
  • Three pounds of bananas cost $7. Complete letter A on the table showing the pounds of bananas at this rate.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!