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
Vikentia [17]
3 years ago
6

Why did he let (y) equals to (1/2 sec t) ? And how did (-1) & (- √2/2) become (2π/3) & (3π/4) ?!!

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
7 0
Just to go into more detail than I did in our PMs and the comments on your last question...

You have to keep in mind that the limits of integration, the interval \left(-1,-\dfrac{\sqrt2}2\right), only apply to the original variable of integration (y).

When you make the substitution y=\dfrac12\sec t, you not only change the variable but also its domain. To find out what the new domain is is a matter of plugging in every value in the y-interval into the substitution relation to find the new t-interval domain for the new variable (t).

After replacing y and the differential \mathrm dy with the new variable t and differential \mathrm dt, you saw that you could reduce the integral to -1. This is a continuous function, so the new domain can be constructed just by considering the endpoints of the y-interval and transforming them into the t-domain.

When y=-1, you have -1=\dfrac12\sec t\implies t=\arcsec(-2)=\dfrac{2\pi}3.

When y=-\dfrac{\sqrt2}2, you have -\dfrac{\sqrt2}2=\dfrac12\sec t\implies t=\arcsec(-\sqrt2)=\dfrac{3\pi}4.

Geometrically, this substitution allows you to transform the area as in the image below. Naturally it's a lot easier to find the area under the curve in the second graph than it is in the first.

You might be interested in
Please help me if you can thank you.
Anarel [89]
X could be 1.5
.........
5 0
3 years ago
Read 2 more answers
What is the slope of the line shown below?
zimovet [89]

Answer: m = 5/8

Step-by-step explanation:

4 0
3 years ago
PLS HELP ASAP<br><br> Solve the equation <br> 1/2x+3/4x=5-2.5x<br> X=_____
Trava [24]

Answer:

1 1/3

Step-by-step explanation:

x = 4/3 or 1 1/3

4 0
2 years ago
Read 2 more answers
HELP!!!!
Lisa [10]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
TIME REMAINING
alekssr [168]

The solution of the equations is (-2, -1)

<h3>System of equation:</h3>

2x - 3y = -1

11x  - 9y = -13

Using elimination method let multiply the first equation by -3.

Therefore,

-6x + 9y = 3

11x - 9y = -13

5x = -10

x = -10 / 5

x = -2

let's find y as follows;

2(-2) - 3y = -1

-4 - 3y = -1

-3y = -1 + 4

-3y = 3

y = 3 / -3

y = -1

learn more on system of equation here: brainly.com/question/1451150

6 0
2 years ago
Read 2 more answers
Other questions:
  • Stan is on a bike ride. His GPS indicates that he has traveled exactly 18 miles and he is 32% complete with his total ride. How
    5·1 answer
  • A triangle has a perimeter of 32 inches. The medium side is 2 more than the short side, and the longest side is 3 times the leng
    11·1 answer
  • If you roll a die three times how many different sequences are possible?
    8·1 answer
  • Which of the following is the method used to determine whether or not a proportion is true?
    12·1 answer
  • (I WILL GIVE BRAINLYIST)
    6·2 answers
  • Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.
    6·1 answer
  • A chord is 10cm from the centre of a circle of radius 15cm. Find the length of the chord.
    7·1 answer
  • $5,000 at a simple annual interest rate of 6.5% for 5 years. What is the total amount of interest Ms. Lee must pay?
    7·1 answer
  • HELPP WHATS THE ANSWERRR
    7·1 answer
  • Plases help help help help
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!