- #1

ozgunozgur

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I am trying to solve these questions for hours :/

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- MHB
- Thread starter ozgunozgur
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- #1

ozgunozgur

- 27

- 0

I am trying to solve these questions for hours :/

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- #2

MarkFL

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Let's begin with the first problem...what have you tried so far?

- #3

ozgunozgur

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Let's begin with the first problem...what have you tried so far?

- #4

MarkFL

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\(\displaystyle e^{y^8}\) ?

- #5

ozgunozgur

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Ah sorry. My third question is true? And second is a bit problem.

\(\displaystyle e^{y^8}\) ?

- #6

ozgunozgur

- 27

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Isn't it gamma function for 8y?

\(\displaystyle e^{y^8}\) ?

- #7

- #8

ozgunozgur

- 27

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Please help me for second question, I guess I have to draw a sketch. Can you draw it full?

- #9

- #10

MarkFL

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Here's what W|A gives for #2:

https://www.wolframalpha.com/input/...+"DoubleIntegral",+"rangestart2"}+->"sqrt(x)"

- #11

ozgunozgur

- 27

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Calculus 2. Please text me steps for my homework. :/ I have no time.

Here's what W|A gives for #2:

https://www.wolframalpha.com/input/...+"DoubleIntegral",+"rangestart2"}+->"sqrt(x)"

- #12

MarkFL

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- #13

I like Serena

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So I think question 2 must also be such a straight forward application.

Looks to me as if the question should read:

$$\int_0^1 \int_{\sqrt x}^1 \exp(y^3)\,dy\,dx=\,?$$

That is, with power $3$, and with the variables of integration swapped.

Now we can solve it by swapping the order of integration, which is likely intended. And yes, a graph may help.

- #14

ozgunozgur

- 27

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I'm not skilled in this part. Please help continue.

So I think question 2 must also be such a straight forward application.

Looks to me as if the question should read:

$$\int_0^1 \int_{\sqrt x}^1 \exp(y^3)\,dy\,dx=\,?$$

That is, with power $3$, and with the variables of integration swapped.

Now we can solve it by swapping the order of integration, which is likely intended. And yes, a graph may help.

- #15

I like Serena

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Please show an attempt to swap the order of integration.I'm not skilled in this part. Please help continue.

Or otherwise give us a clue in some detail where you are stuck.

You should have an example in your textbook that shows how it is done.

If you can't find such an example, you might take a look at this example.

- #16

ozgunozgur

- 27

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Please show an attempt to swap the order of integration.

Or otherwise give us a clue in some detail where you are stuck.

You should have an example in your textbook that shows how it is done.

If you can't find such an example, you might take a look at this example.

- #17

MarkFL

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Reversing the order of integration, we may write:

\(\displaystyle I=\int_0^1\int_0^{y^2} e^{y^3}\,dx\,dy\)

Can you proceed?

- #18

I like Serena

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\begin{tikzpicture}

\filldraw[green!70,draw=gray] (0,0) circle (2.5);

\draw[help lines] (-3.2,-3.2) grid (3.2,3.2);

\draw[->] (-3.4,0) -- (3.4,0);

\draw[->] (0,-3.2) -- (0,3.2);

\draw foreach \i/\x in {-2.5/-a,2.5/a} { (\i,0) node[below] {$\x$} };

\draw foreach \i/\y in {-2.5/-a,2.5/a} { (0,\i) node[ left ] {$\y$} };

\end{tikzpicture}

\[ \iint_D (x^2+y^2)\,dA = \int_0^a \int_0^{2\pi} r^2 \cdot r\,d\theta \,dr \]

- #19

ozgunozgur

- 27

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https://ibb.co/0XxGrDr

https://ibb.co/ZKNtgZy

I rearranged I wonder if I wrote extra or are we going right?

- #20

ozgunozgur

- 27

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.

- #21

ozgunozgur

- 27

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I was sent the other solut. Can you edit these two solving. https://ibb.co/c6S7r8n

- #22

ozgunozgur

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For 2, https://ibb.co/LzqHCyM

For 3, https://ibb.co/BC4kKMp

I don't know if my last solutions going true. Could you write to me?

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