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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
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3 years ago
Six less than x<br>I'm in 8th ​
Fudgin [204]

Answer

I found this. Does this help?

Step-by-step explanation:

If this is an inequality (6 is less than x, or 6 < x), then x is an integer or other value greater than 6.

The variable statement "6 less than x" is (x - 6)

This is a value (variable and constant) where the value of x is determined by an equation

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2 years ago
Complete the statement below to explain how this model shows that 1/6 ÷ 1/4 = 2/3.
svlad2 [7]

Answer:

The answer is 2/3 and I will show the working to prove that in the explanation

Step-by-step explanation:

\frac{1}{6} ÷ \frac{1}{4}

\frac{1}{6}×\frac{4}{1}

Answer =\frac{1}{6}×\frac{4}{1} = \frac{2}{3}

  • So basically what is happening in the above steps what I have shown is that first I am changing the division sign into multiplication and then I am reciprocating the fraction  of 1/4 into 4/1 because on the other side of it is multiplying and after doing that I am simplifying the fraction 4/6 by dividing it  by 2 and hence I got a fraction of 2/3 as the answer
5 0
3 years ago
Read 2 more answers
Suppose that angle COP and angle TOD are vertical angles, the measure of angle COP is 11x-17 and The measure of angle TOD is 9x+
crimeas [40]

The measure of <COD  and <POT are 43 and 43degrees respectively

The point where two lines meet or intersect is known as an angle:

Is <COP and angle TOD are vertical angles, this means that they are equal i.e.

  • <COP = <TOD

Given that:

<COP = 11x - 17

<TOD = 9x + 11

Equate both expressions

11x - 17 = 9x + 11

11x - 9x = 11 + 17

2x = 28

x = 28/2

x = 14

Get <COP

<COP = 11x - 17

<COP = 11(14) - 17

<COP = 154-17

<COP = 137 degrees

Since <COP = <TOD, hence <TOD = 137 degrees

Calculate <COD:

<COD + <TOD = 180

<COD + 137 = 180

<COD = 180 - 137

<COD  = 43 degrees

Also <POT = <COD = 43degrees(vertically opposite angles)

Hence the measure of <COD  and <POT are 43 and 43degrees respectively

Learn more here: brainly.com/question/17247176

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2 years ago
52.85-9.09 rounded to the nearest one
Mkey [24]
53, and 9. Are the answers.
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