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
(6t^4-t+1) - (6t^3-4t)
goldenfox [79]

Answer:

= 6 {t}^{4}   - 6 {t}^{3}  + 3t + 1

Step-by-step explanation:

6 {t}^{4}  - t + 1 - 6 {t}^{3}  + 4t \\  = 6 {t}^{4}   - 6 {t}^{3}  + 3t + 1

5 0
2 years ago
WILL GIVE BRAINLIEST!! Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?
Whitepunk [10]
Slope=4 Point=(1,6)
Y=Mx+b
6=4(1)+b
6=4+b
-4 -4
————
2=b
Equation:4x+2
6 0
2 years ago
What is the conversion?
Gelneren [198K]

Answer:

  see below

Step-by-step explanation:

The conversion factor in the box is the product ...

  \dfrac{1\,\text{kPa}}{1000\,\text{Pa}}\cdot\left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3=10^{-9}\,\dfrac{\text{kPa m}^3}{\text{Pa cm}^3}

_____

The purpose of a conversion factor is to multiply by 1 in the form of a ratio that changes the units. We know that 1000 Pa = 1 kPa, so the ratio (1 kPa)/(1000 Pa) is the ratio of two equal quantities. It has the value 1 and will change units from Pa to kPa.

Likewise, 100 cm = 1 m, so (1 m)/(100 cm) will change the units from cm to m. However the given expression uses cm³, so we need to multiply by the conversion factor 3 times. That factor is ((1 m)/(100 cm))³ = (1 m³)/(10⁶ cm³).

To choose the appropriate conversion factor, look at the units you have (Pa, cm) and the units you want (kPa, m). Find the relationship these have to each other, and write the ratio so that it will cancel the units you have and leave the units you want.

When SI units are involved the prefixes help you out. k = kilo = 1000; c = centi = 1/100. It is worthwhile to get to know them.

8 0
3 years ago
Please help, ASAP!!​
babymother [125]

Answer:

The answer should be  x ≤ 5

3 0
2 years ago
Fill in the numbers that go into the blank boxes. The numbers have to multiply to be the top number and add to be the bottom num
nevsk [136]

Answer: 6 and 6

Step-by-step explanation:6x6=36

6+6=12

3 0
3 years ago
Other questions:
  • Suppose we want to study the average weight of children in the US. We collect a random sample of 345 first graders in three diff
    6·1 answer
  • PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inher
    7·1 answer
  • Explain how you can use the Associative Property to evaluate (7x50)x4.
    9·1 answer
  • What percent is equivalent to 1/20​
    12·2 answers
  • Mr. Schrock is flying an airplane 300 feet above the ground. You were laying on the ground 400 feet from where he dropped a seni
    8·1 answer
  • If 3220 = 80+7, what is the value of c?
    5·1 answer
  • A tube-feeding formula is administered to a patient via Gastrostomy at 75
    7·1 answer
  • Convert the quadratic equation, <br>f (x) = 2(x - 3)2 +1, into standard form.​
    11·1 answer
  • Please someone answer this, “what is the area of triangle ABC?”
    7·1 answer
  • I need help with this question ASAP
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!