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
NISA [10]
3 years ago
13

Find the area of the region bounded by the curves

rmula1" title="y=sin^-1\frac{x}{2}" alt="y=sin^-1\frac{x}{2}" align="absmiddle" class="latex-formula">, y=0, and x=2 obtained by integrating with respect to y. Please include the definite integral and the antiderivative.
Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

π − 2

Step-by-step explanation:

Graph of the region:

desmos.com/calculator/pcascl0frf

If we integrate with respect to x:

∫₀² (y − 0) dx

∫₀² sin⁻¹(x/2) dx

But we want to integrate with respect to y.  Let's start by finding the new limits of integration.

y = sin⁻¹(x/2), so when x = 0, y = 0.  When x = 2, y = π/2.

Next, we need to find x in terms of y.

sin y = x/2

x = 2 sin y

So the integral with respect to y is:

∫₀ᵖⁱ² (2 − x) dy

∫₀ᵖⁱ² (2 − 2 sin y) dy

Integrating:

(2y + 2 cos y + C) |₀ᵖⁱ²

(π + 2 cos (π/2) + C) − (0 + 2 cos 0 + C)

(π + 0 + C) − (0 + 2 + C)

π − 2

You might be interested in
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute,
yan [13]

we are given with two equations: R=143-0.65a for women and R = 165-0.75a for men. In this prblem we are asked the age of a man when R is equal to 135. In this case, we use the second equation and substitute R with 135. In this case, 135 = 165 - 0.75 a; a is equal then to 40 yrs old. In 2, when x is equal to 4, then 0.5*4 + 3 is equal to 5. 
6 0
3 years ago
Find the distance between the given points (2,8) and (7,7)
Ray Of Light [21]

Answer:

d=\sqrt{26}\approx5.0990

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula.

The distance formula is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Let (2,8) be x₁ and y₁ and let (7,7) be x₂ and y₂. Thus:

d=\sqrt{(7-2)^2+(7-8)^2}

Simplify:

d=\sqrt{5^2+(-1)^2}

Square:

d=\sqrt{25+1}

Add:

d=\sqrt{26}\approx5.0990

And that's our answer :)

6 0
3 years ago
What is 9/10 divided by 3/5
Paha777 [63]

Answer:

1 /2 or 1.5

Step-by-step explanation:

Dividing fractions are relatively easy. One way to do it is multiplying the reciprocal of one of the fractions to the other. So 3/5 would become 5/3. Multiply, 9/10*5/3=45/30. Now that you have the answer you need to simplify which will end up into 1 1/2.

7 0
3 years ago
Read 2 more answers
What is 7a^{2} - a^{2} + 16
prohojiy [21]

Answer:can u pls help answer my question 4d+15 is greater than or equal to -1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What’s 124 divided by 7440
Bingel [31]
It’s 0.016666666666667
5 0
3 years ago
Read 2 more answers
Other questions:
  • Provide a clear answer while explaining how to do each step to the question below:
    5·1 answer
  • What is 2,117 divided by 3
    5·1 answer
  • D.153.86in.............
    6·1 answer
  • Factorize using middle term:<br> m²+3m+2
    15·1 answer
  • How to find the percent?
    13·2 answers
  • One canned juice drink is20%
    6·1 answer
  • Which is a factor of f(x) = 60x^4 + 86^3 - 46x^2 - 43x + 8
    11·2 answers
  • PLS HELP! WILL GIVE BRAINLIEST
    11·1 answer
  • Explain the impact of planes and pulleys on work and force. Select the facts that are accurate.
    7·1 answer
  • You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!