My Homework - Can You Help Me?

ozgunozgur

New member
I am trying to solve these questions for hours :/

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MarkFL

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

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MarkFL

Staff member
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
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
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
I did question 2. Is it true? Can you help me?

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ozgunozgur

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

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MarkFL

Staff member
What course is this for?

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

ozgunozgur

New member
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

Staff member
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
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
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.

Klaas van Aarsen

MHB Seeker
Staff member
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
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

Staff member
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:

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
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
Thank you very much.
I rearranged I wonder if I wrote extra or are we going right?

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