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
kiruha [24]
3 years ago
6

Evaluate the integral by changing to polar coordinatesye^x dA, where R is in the first quadrant enclosed by the circle x^2+y^2=2

5
Mathematics
1 answer:
34kurt3 years ago
7 0
\displaystyle\iint_Rye^x\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=5}r^2\sin\theta e^{r\cos\theta}\,\mathrm dr\,\mathrm d\theta

which follows from the usual change of coordinates via

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

and Jacobian determinant

|\det J|=\left|\begin{vmatrix}\mathbf x_r&\mathbf x_\theta\\\mathbf y_r&\mathbf y_\theta\end{vmatrix}\right|=|r|

Swap the order, so that the integral is

\displaystyle\int_{r=0}^{r=5}\int_{\theta=0}^{\theta=\pi/2}r^2\sin\theta e^{r\cos\theta}\,\mathrm d\theta\,\mathrm dr

and now let \sigma=r\cos\theta, so that \mathrm d\sigma=-r\sin\theta. Now, you have

\displaystyle\int_{r=0}^{r=5}\int_{\sigma=0}^{\sigma=r}re^\sigma\,\mathrm d\sigma\,\mathrm dr=\int_{r=0}^{r=5}r(e^r-1)\,\mathrm dr=4e^5-\dfrac{23}2
You might be interested in
Capturing nature’s emotion and energy, as seen in this painting by Monet and heard in Debussy’s “The Snow Is Dancing,” is a typi
Colt1911 [192]
A : Renaissance is correct
5 0
3 years ago
Read 2 more answers
Ronald is trying to reconstruct his spending pattern from May. He knows that he had $315 in his account on May 1, but after that
Valentin [98]

Answer: C. Ronaldo overviewed his account twice.

Step-by-step explanation:

Just took a test on edge.

7 0
3 years ago
Read 2 more answers
What is the equation of a line with a slope of 4 and a y-intercept of 2?
Trava [24]

Answer:

y=4x+2 or f(x)=4x+2

Step-by-step explanation:

This is because the equation format for a line is y=mx+b, the slope is m and the y-intercept is b. So all you have to do is fill it out to get y=4x+2. Or the other way I listed the equation is right too. Hope this helps!

6 0
3 years ago
Read 2 more answers
X^2-10x+8=0 by completing the square
OverLord2011 [107]
When completing the square <span>x=9.12311 and </span><span>x=<span>0.876894</span></span>
4 0
3 years ago
PLS HURRY GIVING BRAINLIEST
AlexFokin [52]

Answer:

150Ft^2

Step-by-step explanation:

The area of a parallelogram is A=BH where B is base length and H is height. I'm not sure why there is information about a triangular base, maybe an illustration would help. But with the information provided, the base times  height is equal to 150 Ft^2. Check out the Kahn Academy video for a better explanation  

5 0
2 years ago
Read 2 more answers
Other questions:
  • Help plz
    9·2 answers
  • Light travels at 186,000 miles per second. How many FEET does it travel in a microsecond? (A microsecond is a millionth of a sec
    14·1 answer
  • Andy loves taking notes. He started the school year with 45 pages of notes from last year and he plans to take 2 pages of notes
    7·1 answer
  • The cost per minute for a conference phone call originally 2.60 increased by 30% what is the new price?
    15·2 answers
  • A carpenter has boards of lengths 24, 40, and 48 inches that must be cut into smaller boards of equal length, with no scrap wood
    11·1 answer
  • A town received 1/2 inch of rain in 1 1/3 hours.what was the average rate of rainfall for the town in inches per hour?
    9·1 answer
  • Is 43 a composite number
    6·1 answer
  • Here this is for CHELSEA
    8·2 answers
  • The cost of a concert ticket last week was $50.00. This week a concert ticket is $55.00. The percent increase of the ticket from
    7·1 answer
  • F(x)=3x^2+2x-3 and g(x)=2x+4. Identify the rule for f+g
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!