/sci/ - Science & Math

Nevermind, I did it myself. I actually graphed it and see how it makes sense. Now I see where I made the error.

Thank you so much, dude. You helped me out a lot and refreshed my mind on some forgotten concepts. Appreciate it.

The thread can die or whatever. Like I said previously, thank you.

>>1073660
>>1073660
>>1073660
>>1073660
>>1073660
>>1073660
>>1073660
>>1073660
>>1073660

DON'T EVEN
FUCKING
KNOW
HOW
THAT'S
POSSIBLE

I'M STARING RIGHT AT IT.

>>1073627

Exactamundo. I made the limits as pi/3 and -pi/3, because if we measure the angles of the region R, aka the circle, we see that it is sixty degrees(pi/3). I follow the graphical method, so that may be my flaw here. I'm not sure how I'm wrong either, since I see my textbook showcases similar problems and uses the SAME exact method. It's so bizarre.

>>1073595

Learned the basics of Calc at age 14(derivatives), but didn't know about the concepts like Rolle's Theorem, Mean Value Theorem, the concept of Limits, etc until I was 19. From then on, I learned Calc 2, 3 and Linear Algebra after 19. I'm 21 now.

By the way, I was homeschooled; so, don't be surprised at the young age.

>>1073573
>>1073543

Now we're talking.

Since an answer exists, I'm guessing that there -is- enough information in the text to solve/figure it out. I'll even tell you what it says:

"In Exercises 7-12, use a double integral to find the area of the indicated region."

They say that area is 9π; I keep getting 6π + (9√3)/2. If my limits of integration are wrong, fine; but how so? I'm measuring from the Origin to 6 cos theta. So, aren't the fixed boundaries for r going to be 0 and 6 cos theta?

For the angle, it's a bit different for me to explain. I can't put it in words, but what do you think?

Took me about 3/4 months to learn those subjects, OP. Before taking any class, I usually study ahead of time and I'm already in the middle of the syllabus by the time the class starts. The rest of the semester, I'm pretty much solidifying everything I know and making sure I understand the concept(s)/everything is concrete.

But, to answer your second question:

I learned it myself and from class. 80% myself; 20% from class.

I use hard-cover books. Thomas Calculus, Larson & Hosteller Calculus Alt. 6th Edition, etc.

Khan Academy is good, but I also go to Pauls Online Notes.

>>1073487

>Based on my method.

Considering that this is a problem from the book, that comment/useless verbal strike is utter bullshit. Furthermore, this isn't one of those problems where you're clearly given a DIRECT integral to solve. With this problem, I have to actually create the integral with the proper limits and then solve.

Instead of resorting to verbal attacks, which don't amount to anything since we'll never meet one another irl, try to actually help me out with the problem or understand it another way. Either/or, it's a win-win for you since you can get the right answer, puff your chest and show 'who is boss.'

The one time there's a non-Algebra thread and all I receive are arguments. =|

>>1073429

>Calculus III.
>Calculus textbook.
>Also taught/reviewed in higher-end upper division Math classes.
>Most of all, MATH MAJOR.
>Said this a thousand times.

Oh boy.

>>1073409

They give me r = 6 cos theta automatically. It's right above the picture in the textbook. The only thing I've added are the red lines to measure the angle. They're essentially telling me that's r2 and I have to find the rest of it myself.

>>1073418

Go to the link. There's an entire graphical process done here to configure angles. I understand what you're saying, but it isn't retarded; it makes sense, in a cooky way, if you've done it before.

>>1073374

http://www.math.umn.edu/~nykamp/m2374/readings/changevardint/

Here, read that. That shows a similar example.

They're able to understand, conceptually, that the angle is from 0 to 2pi, simply because g(x,y) is circular and spans the Cartesian plane. As a rule, we measure the angle from 0 and stop at 2pi(for this particular problem). That's how we conceive theta1 as 0 and theta2 as 2pi. For r, r1 = 0; r2 = 7 since r acts as the hypotenuse / range of g(x,y).

Can anyone else lend a helping hand?

>>1073321

That's the fucking point of this problem. When I took Calc III, I was just GIVEN these type of graphs and you had to find the limits of integration by graphically analyzing it.

We can see that r goes from 0 to 6 cos theta because 'r' begins from Origin and stops at the given point. That's one thing I'm completely sure about; the angles, however, I'm a bit unsure about. When I did similar problems in my other text, I got them right. This text, I'm getting them wrong. It's frustrating.

>>1073317

How am I being a prick about it? Those 'red lines' were drawn by me to measure the angle of the region R.

>>1073302

...

Then, there's nothing else to say? I've explained the problem and provided an image. In the book, they don't even give the limits of integration; they just give the circle on the Cartesian plane. If you think my picture is dull looking, the book is worse.

Does anyone else have anything to contribute? =| I'm seriously perturbed by this problem.

>>1073211

It isn't shitty at all. The book has that exact image, more or less. The 'red' lines drawn is my measurement, but the circle is on the Cartesian plane.

Is this picture better? It's .. friendlier?

I'm going to bump this thread until you like it. =| At the moment, all my friends are asleep and I've been staring at this problem for the past 20 mins. I know some of you mathfags are out there, snickering at this fucking problem.

>>1073192

Thanks, I appreciate it. You'll have fun with it; promise.

Anyone else care to help me out? The problem itself is not that difficult, I just want to know exactly WHERE I went wrong/detoured.

>>1073154

This is Calc III material mainly, but it's reviewed in other higher-end courses as 'refresher' material. It's essentially the end of Calc III. It was for me, at least. I learned it near the end of the semester last Fall.

>>1073135

If this was a Homework thread, I would've posted the problem without knowing shit. Given the information I've included, I know a little something about the subject and I'm simply perplexed at a small issue. I just want some insight by another Mathfag to see where/how I went wrong.

Bumping thread because I really want to get this answered/settled. The same dilemma persists in the other review problems. When I do other problems in my other Calculus textbook, I seem fine. These problems are giving me some trouble.

Hey, /sci/. I need some help here. Concurrently, I'm on vacation/summer break, but I always try to practice every now and then to keep myself sharp and prepare myself for the next Mathematics class. However, I'm having a bit of difficulty with a few review problems. Some, probably most of you, have seen me post here before, so you definitely know this isn't some homework/test thread; it's honestly just an inquisitive thread for mathheads, in general. I'm trying to just get my mind back into gear for next semester because my next class deals with these integrals like nothing.

Anyway, back to the problem:

The problem asks me to compute the region R, denoted by the circle, with a double integral. Of course, I use Fubini's theorem(aka, polar coordinate double integral form) and through graphical inspection, found the limits of integration:

θ1 = π/3; θ2 = -π/3
r1 = 0; r2 = 6 cos θ

After all was said and done, I found the answer to be 6π + (9√3)/2. I even verified this on Wolfram, which gave me the exact answer. When I check the answer in the book, however, it's 9π. My question is this:

How? Did I make a calculation error whence performing the limits of integration? The degree looks to be sixty degrees, and it can't be ninety or anything higher. Could it be from 0 to π/3? If so, why is this true?

Anyone's welcome for input. I'd appreciate anything. In fact, general Math thread for all.

>>1072282

I felt like that with Physics. I learned that I enjoyed the idea and mysticism of Physics(i.e., Fenyman, Einstein, etc), but not the particular rigor behind it. With Mathematics, I enjoy both the rigor and mysticism. I've always loved Mathematics and I chose that as my primary goal, so it's win-win for me.

For me, Chemistry wasn't so bad. I just disliked the laboratory assignments; otherwise, I consistently scored into the top 80s / 90s on tests. Then again, my Mathematics background helped me out a lot. The concepts weren't too difficult to comprehend because I understood the mathematical laws associated with them, so even if I was confused with one aspect of the concept, I could always 'read' the mathematical equation and find it there.

>>1071766

>Engineers and Physicists have to take that course.

Exactamundo.

>my face when I realized this after the semester.

>>1071720

I'm a Mathematics major, but check this out:

I learned later on, after I took the class, I could've taken Algebraic-based Physics because the Physics I took was specifically for Engineers/Computer Scientists. It was a prerequisite for them; it wasn't a pre-req for me. The credits were still applicable to my major, but everyone I know looks at me with this, "ROFL FUCKING DUMB" look. Remember, kids; always get advised by a knowledgeable professor. If you advise yourself, like I did, you run the risk of making horrific mistakes like that.

To be honest, that Physics and the previous one(Classical Mechanics) dropped my GPA down dramatically. In the first class, Phys 1, I scored a B. In this one, I scored a C. I could've easily scored two A's in the algebraic-based Physics courses. What stung even more is that my professor for E&M looked at me inquisitively as to why the fuck I took the course if I had no reason to be an engineer/physicist/computer scientist.

Pretty much one of the most depressing aspects of my entire College career. I plan to take algebraic physics 1 and 2 just for the fuck of it so I can get the extra A's on my record.

Electricity and Magnetism.

That class had me in tears -- Literally. I cried almost every other weekend. The tests were hard as fuck, calculators weren't allowed and we essentially had to use concepts/physical principles to solve the problems. The problems on the test were barely familiar to the homework and he would introduce geometric figures that the class just didn't have experience with. I remember on the final he wanted us to find the current and resistance on a tetrahedron. Those were particularly difficult because we had to deal with 3-Dimensional structures. Well, think about it that way at least.

Tests were worth between 150 and 250; he also didn't believe in partial credit or curving the grade. I remember for one test I received a 80 out of a possible 250. Another classmate of mine received a 5 out of 250. Two others received 25 out of 250. That class was so difficult. I barely passed with a C and was happy I received A's and B+'s in my other classes to balance out that class(4 credits).

Just thinking about it gives me the shivers.