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My Homework - Can You Help Me?

ozgunozgur

New member
Jun 1, 2020
27
I am trying to solve these questions for hours :/

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MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
Let's begin with the first problem...what have you tried so far?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
Yes, I agree with your finding of a minimum at \((2,-1)\). It is a global minimum. For the second problem, isn't the integrand:

\(\displaystyle e^{y^8}\) ?
 

ozgunozgur

New member
Jun 1, 2020
27
Yes, I agree with your finding of a minimum at \((2,-1)\). It is a global minimum. For the second problem, isn't the integrand:

\(\displaystyle e^{y^8}\) ?
Ah sorry. My third question is true? And second is a bit problem.
 

ozgunozgur

New member
Jun 1, 2020
27
Yes, I agree with your finding of a minimum at \((2,-1)\). It is a global minimum. For the second problem, isn't the integrand:

\(\displaystyle e^{y^8}\) ?
Isn't it gamma function for 8y?
 

ozgunozgur

New member
Jun 1, 2020
27
I did question 2. Is it true? Can you help me?
 

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ozgunozgur

New member
Jun 1, 2020
27
Please help me for second question, I guess I have to draw a sketch. Can you draw it full?
 

ozgunozgur

New member
Jun 1, 2020
27
Can you review my answer?
 

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MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
What course is this for?

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

 

ozgunozgur

New member
Jun 1, 2020
27
What course is this for?

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

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

MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
The use of exponential integral and gamma functions goes beyond what I was taught in Calc 2. We did multi-variable calculus in Calc 3, but still worked with elementary functions. I can't help you with this problem. Perhaps someone else can.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,736
Questions 1 and 3 are fairly straight forward applications of multivariable Calculus with elementary functions.
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.
 

ozgunozgur

New member
Jun 1, 2020
27
Questions 1 and 3 are fairly straight forward applications of multivariable Calculus with elementary functions.
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.
I'm not skilled in this part. Please help continue.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,736
I'm not skilled in this part. Please help continue.
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 text book that shows how it is done.
If you can't find such an example, you might take a look at this example.
 

ozgunozgur

New member
Jun 1, 2020
27
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 text book that shows how it is done.
If you can't find such an example, you might take a look at this example.
 

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MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
Now that Klaas has figured out what #2 is actually supposed to be, let's look first at the region over which we are to integrate:

mhb_0017.png

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?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,736
For question 3 we should use a switch to polar coordinates:
\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}
\[ \iint_D (x^2+y^2)\,dA = \int_0^a \int_0^{2\pi} r^2 \cdot r\,d\theta \,dr \]
 

ozgunozgur

New member
Jun 1, 2020
27

ozgunozgur

New member
Jun 1, 2020
27
.
 

ozgunozgur

New member
Jun 1, 2020
27

ozgunozgur

New member
Jun 1, 2020
27