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
zhenek [66]
3 years ago
13

Sin(x2 y2 da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 5

Mathematics
1 answer:
Rudik [331]3 years ago
3 0
I assume there's a plus sign missing above...

Convert to polar coordinates, using

\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}

Then the Jacobian is

\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r

Then

\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta

so the integral can be written as

\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta

Let s=r^2, so that \dfrac{\mathrm ds}2=r\,\mathrm dr.

\displaystyle\frac12\int_0^{\pi/2}\int_1^{25}\sin s\,\mathrm ds\,\mathrm d\theta=-\frac12(\cos25-\cos1)\int_0^{\pi/2}\mathrm d\theta=\frac\pi4(\cos1-\cos25)
You might be interested in
Irina predicted that she would sell 75 books, but she actually sold 95 books. Which expression would find the percent error?
dolphi86 [110]

Answer:

d

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is the square root of 49 if it is then multiplied by 14 and divided by pi?
AlekseyPX
The square root of 49 = 7 if it is multiplied by 14 and divided by pi, it would equal 31.194, which would be 31.19. 
8 0
3 years ago
A jogger traveled at the speed of 8 km/h for 15 minutes.How <br> far did she run
pickupchik [31]
The magic triangle is D and S and T where D is over S and T so if D is over s and t u dived and if the question is looking for D you would multiply S and T so 8 is the S i'm guessing and 15 is the T so ur gonna be looking for D so D=120 S=Speed D=Distance and T=time 
i hope i helped you good luck   
5 0
3 years ago
Area of the living room is 180 square feet and the perimeter is 54 feet. What are the dimensions in feet?
dolphi86 [110]

Answer.....15ft by 12ft

Explanation:

Area = Length × Width

180 = LW....make W the subject of formula

;W = 180/L

Perimeter = 2L + 2W

54 = 2L + 2(180/L)...sub W with the formula above...

then simplify the equation and obtain...

2L^2 - 27L + 180 = 0....then solve using the quadratic formula....then obtain..

;L = 15ft....after obtaining L = 15...then substitute into the W = 180/L equation...

where W = 180/15 = 12ft

there you have...Length = 15ft and Width = 12ft

5 0
3 years ago
Can someone plz help me out
Shkiper50 [21]
2.false. This is so as 3 to 4 or 3/4=0.75 while 4 to 3 is 1.333333333333333 infinite. 
7 0
3 years ago
Other questions:
  • Determine which relation is a function.
    15·1 answer
  • A bank advertises an interest rate of 4% per year, compounded monthly
    13·1 answer
  • I don’t know how to solve for p.
    14·1 answer
  • A successful basketball player has a height of 6 feet 9 ​inches, or 206 cm. based on statistics from a data​ set, his height con
    10·2 answers
  • Staci is attending a music festival. The tickets at the festival cost $87.96. Staci plans to purchase $30 T-shirts from the even
    5·1 answer
  • What is the absolute value of 8.15
    15·1 answer
  • BRAINIEST TO WHOEVER RIGHT
    12·2 answers
  • Please someone help me out
    6·1 answer
  • Identify the terms in the expression 70 – (4 • 15).
    13·2 answers
  • So my grades keep going down <br> Whats the best way to study
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!