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sashaice [31]
2 years ago
12

Evaluate the following​ integral, where R is bounded by ​, ​, and . Question content area bottom Part 1 enter your response here

​(Simplify your​ answer.)
Mathematics
1 answer:
Volgvan2 years ago
7 0

\iint_{R} y^{2} d A=\int_{x=-2}^{3} \int_{y=-x-2}^{3 x+6} y^{2} d x d y d x

\text { (taking Strip as shown). }

=\int_{-2}^{3}\left(\frac{y^{3}}{3}\right)_{-x-2}^{3 x+6} d x

=\frac{1}{3} \int_{-2}^{3}(3 x+6)^{3}-(-x-2)^{3} d x

\begin{gathered}=\frac{1}{3}[4375]=\frac{4375}{3} \\=1458.33\end{gathered}

What is integral ?

  • Calculating an integral is called integration.
  • Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc.
  • When we discuss integrals, we often refer to definite integrals.
  • For antiderivatives, indefinite integrals are utilized.
  • Apart with differentiation, integration is one of the two main calculus subjects in mathematics (which measure the rate of change of any function with respect to its variables).
  • It's a broad subject that is covered in courses at the higher grade levels, such classes 11 and 12.
  • Broadly speaking, integration by parts and via substitution is explained.
  • You will discover the definition of integrals in mathematics, the integration formulae, and examples here.

So the more about integral visit.

brainly.com/question/2289273

#SPJ4

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Cuantos minutos hay de diferencia entre 4.8 h y 5 h​
gayaneshka [121]

Answer:

4.1 horas 246 min

4.7 horas 282 min

4.8 horas 288 min

4.9 horas 294 min

5 horas 300 min

Step-by-step explanation:

5 0
3 years ago
The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p
Colt1911 [192]
The boundary of the lawn in front of a building is represented by the parabola

y = (x^2) /16 + x - 2

And you have three questions which require to find the focus, the vertex and the directrix of the parabola.

Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).

1) Focus:

It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).

In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)

Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k

What we need is to complete a square. You can follow these steps.

1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]

2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>

16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]

3) The three first terms inside the square brackets are a perfect square trinomial: =>

(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2  - 96] =>

(1/16) [(x+8)^2 ] - 96/16 =>

(1/16) (x +8)^2 -  6

Which is now in the form a(x - h)^2 + k,
where:

a = 1/16 , h = - 8, and k = -6

(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

=> a = 1/16 => p =1/4a = 16/4 = 4
 
y-componente of the focus = -6 + 4 = -2

x-component of the focus = h = - 8

=> focus = (-8, -2)

2) Vertex

We found it above, vertex = (h,k) = (-8,-6)


3) Directrix

It is the line y = p units below the vertex = > y = -6 - 4 = -10

y = -10   

 


4 0
3 years ago
Plz answer my question quickly!!!!! First person to respond will get brainliest!!!!!
garri49 [273]

Answer:

The Correct and final Answer Is

D) Or option 4

Hope this helps!

Please mark brainliest!

Bye!

4 0
3 years ago
Read 2 more answers
Which of the following expressions is equal to 1 divided by 16
Mama L [17]

Answer:

8

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
5
natulia [17]

Answer:

1648

Step-by-step explanation:

5/9 are girls. The 9 represents the total.

Set up a proportion and you have

5/9 = ?/3708

3708/9=412

412x5= 2060 girls

3708-2060= 1648

8 0
3 years ago
Read 2 more answers
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