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
Setler [38]
3 years ago
14

Evaluate the integral Integral from 0 to 1 Integral from 0 to 3 Integral from 3 y to 9 StartFraction 6 cosine (x squared )Over 5

StartRoot z EndRoot EndFraction dx dy dz by changing the order of integration in an appropriate way.
Mathematics
1 answer:
Natalka [10]3 years ago
6 0

Answer:

\int^1_0\int^3_0\int^9_{3y}\frac{6 cos x^2}{5\sqrt z}dxdydz =\frac{18}{5}(1+\frac{sin2}{2})

Step-by-step explanation:

cosine x²= cos x²

Rule

  • \int x^ndx= \frac{x^{n+1}}{n+1}+c
  • \int cos \ mx \ dx = \frac{sin \ mx}{m}+c
  • \int \frac{1}{\sqrt x}dx = \frac{\sqrt x}{\frac{1}{2}}  +c= 2\sqrt x+c

Given that,

\int^1_0\int^3_0\int^9_{3y}\frac{6 cos x^2}{5\sqrt z}dxdydz

=\int ^1_0[\int^3_0(\int^9_{3y} \frac{6cos x^2}{5\sqrt z}dz)dy]dz

=\int^1_0[\int^3_0([\frac{6cos x^2 \times \sqrt z}{5\times \frac{1}{2}}]^9_{3y})dy]dx

=\int^1_0[\int^3_0([\frac{12cos x^2 \times( \sqrt 9-\sqrt{3y})}{5}])dy]dx

=\int^1_0[\int^3_0([\frac{12cos x^2 \times( 3-\sqrt{3y})}{5}])dy]dx

=\int^1_0[\frac{12cos x^2 \times( 3y-\frac{\sqrt{3}y^\frac{3}{2}}{\frac{3}{2}})}{5}]^3_0dx

=\int^1_0[\frac{12cos x^2 \times( 3.3-\frac{2\sqrt{3}.3^\frac{3}{2}}{3})}{5}]^3_0dx

=\int^1_0[\frac{12cos x^2 \times( 9-6)}{5}]dx

=\frac{18}{5}\int^1_02cos x^2dx

=\frac{18}{5}\int^1_0(1+cos2x)dx

=\frac{18}{5}[(x+\frac{sin2x}{2})]^1_0

=\frac{18}{5}(1+\frac{sin2}{2})

You might be interested in
Which is the least positive integer that should be multiplied with 2 × 2 × 2 × 3 so that we get
Elan Coil [88]

Answer:

3

Step-by-step explanation:

In order to have a perfect square you have to have at least two prime factors, and since three is quite clearly not in a pair, the answer is three.

8 0
2 years ago
2x-1<br> Evaluate the algebraic expressions for the given values of the variable
igor_vitrenko [27]
<span>An algebraic expression is an expression constructed from a number of constants and variables utilizing algebraic operations. These algebraic operations are addition, subtraction, multiplication, division, and exponentiation. A constant is constant, so its value is unchanged. A variable changes based on the value provided. In the provided example, 2x-1, there are two constants, "2" and "1", and one variable "x." The algebraic operations utilized are multiplication and subtraction. In order to evaluate the value of the algebraic expression, the given value for the variable must be substituted for the variable x, and then the algebraic operations executed to obtain the answer. For instance, if you were told that the value of x in this case was 2, then you would substitute the value 2 for x and perform the described operations. Remember to follow the order of operations when evaluating an algebraic expression! 2x-1 for x=2 2(2) - 1 4 - 1 3 is the answer. Remember, even though the multiplication operation is not explicitly stated, it is implied that a constant attached to a variable (termed a coefficient) is multiplied with the value of the variable.</span>
5 0
2 years ago
А bag contains 3 red, 4 blue, and 2 green chips. Two
Lelechka [254]

Answer:

1/9

Step-by-step explanation:

3+4+2=9

9*2=18

18/2=2/18

2/18=1/9

3 0
3 years ago
Solve the problem please
Molodets [167]

Answer:

x = 9±sqrt(7)

Step-by-step explanation:

3(x-9)^2 =21

Divide each side by 3

3/3(x-9)^2 =21/3

(x-9)^2 =7

Take the square root of each side

sqrt((x-9)^2) =±sqrt(7)

x-9 =±sqrt(7)

Add 9 to each side

x = 9±sqrt(7)

4 0
2 years ago
Sandeep used 8 litres of fuel to travel 76 miles.
OleMash [197]

Answer:

I got, when calculated, 209 miles. (It may be wrong)

Step-by-step explanation:

First, I calculated how many miles can Sandeep travel with 1L, therefore I divided 76 miles by 8L and got 9.5 miles on 1L.

Then I multiplied 9.2 miles by 22L and got 209 miles.

This may be wrong but if anyone else is able to work it out much appreciated if it's correct.. Your most welcome!

4 0
2 years ago
Other questions:
  • Describe two different ways that you could find the product 8 x 997 using mental math. Find the product and explain why your met
    10·1 answer
  • Is triangle ABC similar to triangle DEF? why or why not.
    6·1 answer
  • Basma cuts ribbon to its onto balloons for the carnival. She has 925.6 inches of ribbon in all. If each ribbon must be 24 inches
    7·1 answer
  • What is the value of x
    11·1 answer
  • How do I find the hypotenuse of a triangle when given 90 degrees and one side length?
    15·1 answer
  • A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection
    15·1 answer
  • How many points did Deven score in his 6th game?
    7·1 answer
  • Y = n(n + 1)<br><br> please help, thanks!!!
    7·1 answer
  • In a company, 37‰ of the 1500 employees are female. how many are male?
    13·1 answer
  • Find the measure of x.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!