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How Do You Do This Integral?  
User currently offlineHSV From Australia, joined Sep 2001, 171 posts, RR: 0
Posted (10 years 6 months 6 days 18 hours ago) and read 553 times:

Can someone integrate this:
(4 + cosx)^0.5 (i.e. square root of 4+cosx)
with respect to x.

Thanx in advance.

15 replies: All unread, jump to last
 
User currently offlineI Like To Fly From United States of America, joined Feb 2001, 1188 posts, RR: 2
Reply 1, posted (10 years 6 months 6 days 17 hours ago) and read 527 times:

Now why did we have to learn that crap in school? I seriously believe high school math is pointless & like 1 in 10,000 people will use it in life. It should be an optional in college if you want to go into a field where you will need it. But anyway, I can't help... im just ranting. I managed a 92 in math, however I also managed to fill my mind with more important information after the final exam... you know, like porn. Smile

User currently offlineDelta-flyer From United States of America, joined Jul 2001, 2676 posts, RR: 9
Reply 2, posted (10 years 6 months 6 days 17 hours ago) and read 519 times:

HSV.... this looks very difficult. Are you sure you have the correct problem statement?

My first thought is to see if an identity exists that would simplify the 4+cosx. If it were 1+cosx, we'd be in business (1+cosx = 2cos^2(0.5x)).

My second thought is that this may resemble an elliptic integral of the second kind. But alas, checking in one of my college math books, that would be of the form (1-k^2 sin^2 x)^0.5 -- close, but no cigar, unless you can find some trig identity that would get it into this form. In any event, elliptic integrals do not have closed form solutions, and they are always definite integrals.

I'll sleep on it tonight. My college freshman son is also contemplating it.

As far as I_Like_To_Fly's comment, just ignore it. Many people use math in their lives, particularly engineers. If you have an aptitude for it, you should study it, because a good comand of math will set you apart from the majority of graduates who will be competing with you for high paying jobs.

Cheers,
Pete


User currently offlinePanAm747 From United States of America, joined Feb 2004, 4242 posts, RR: 11
Reply 3, posted (10 years 6 months 6 days 16 hours ago) and read 515 times:

No offense Delta-flyer but I doubt you use this stuff either. If you saw this you would probably throw it into Matlab or Maple or something. I seriously doubt you would ever do this math by hand in your job. As they say, that's why God made computers.


Pan Am:The World's Most Experienced Airline - P(oor) S(ailor's) A(irline): San Diego's Hometown Airline-Catch Our Smile!
User currently offlineChrisair From United States of America, joined Sep 2000, 1461 posts, RR: 4
Reply 4, posted (10 years 6 months 6 days 16 hours ago) and read 511 times:

Yes, that's why God made computers...and calculators...

Anyway, i did it and the answer I got was ((cos(x)+4)^0.5)dx. Do you need it taken down another step?

User currently offlineI Like To Fly From United States of America, joined Feb 2001, 1188 posts, RR: 2
Reply 5, posted (10 years 6 months 6 days 16 hours ago) and read 505 times:

Many people use math in their lives

Hardly anyone on this planet does advanced algebra or trig by hand in their lives. If they need to do it for some god awful reason then the few people who do know it for their entire lives have written computer programs for the rest of us. It is stupid to learn it unless you have a particular reason that 99% of us don't need.

User currently offlineHSV From Australia, joined Sep 2001, 171 posts, RR: 0
Reply 6, posted (10 years 6 months 6 days 15 hours ago) and read 499 times:

Thanks for your reply Delta-Flyer.

The question is actually from a friend so I don't know if he got the question down correctly. I haven't done trig integrals for about 2 years. The only integrals I ever use now are related to statistical distributions and stochastic processes.

Chrisair, I got that answer too but you forgot the constant! Great minds think alike!  Big thumbs up

User currently offlineFlyf15 From , joined Dec 1969, posts, RR:
Reply 7, posted (10 years 6 months 6 days 14 hours ago) and read 495 times:

In short, you can't do it  Smile/happy/getting dizzy

Unless I'm forgetting how to do this math (I'm sitting here with both my Calc 2 and Calc 3 books on my lap, its been a while) ...you can't subsitute it out to the point where it becomes solvable.

User currently offlineIhadapheo From United States of America, joined Sep 2001, 6024 posts, RR: 62
Reply 8, posted (10 years 6 months 6 days 14 hours ago) and read 492 times:

Isn't this like the answer to "Life the Universe and everything" being 42


Pray hard but pray with care For the tears that you are crying now Are just your answered prayers
User currently offlineIkarus From United Kingdom, joined Jan 2001, 3524 posts, RR: 3
Reply 9, posted (10 years 6 months 6 days 13 hours ago) and read 489 times:

The answer is: Numerically....

Regards

Ikarus

User currently offlineDelta-flyer From United States of America, joined Jul 2001, 2676 posts, RR: 9
Reply 10, posted (10 years 6 months 6 days 3 hours ago) and read 470 times:

Anyway, i did it and the answer I got was ((cos(x)+4)^0.5)dx. Do you need it taken down another step?

Chrisair, you did not do anything, just restated the problem. Now integrate that function! (HSV just neglected the ( )dx, but of course it was understood to be there.)

Now, I am not going to argue with you guys about the desirability of learning advanced math. You can solve most everyday problems by computer, of course, but you will not move forward without understanding the underlying principles. And yes, I did use math extensively when I worked in engineering. I designed electro-hydraulic control systems for rotary actuators and controls for hydraulic pumps. These involve differential equations, Laplace transforms and extensive use of complex variables. However, in the last few years I have been doing management of engineering programs and sales, so I am getting rusty in the math.

You guys suit yourselves, it's your lives and careers. Take the easy road, that's the modern way!

Cheers,
Pete




User currently offlineKlmfan From Austria, joined Jun 2001, 445 posts, RR: 5
Reply 11, posted (10 years 6 months 3 days 4 hours ago) and read 452 times:

I would do it that way:

(4 + cosx)^0.5 dx=

= [(4+cosx)^3/2]/3/2 =

= 2/3 (4+cosx)^3/2

I'm not quite sure, it's been a long time since I needed integrals...



User currently offlineDelta-flyer From United States of America, joined Jul 2001, 2676 posts, RR: 9
Reply 12, posted (10 years 6 months 3 days ago) and read 447 times:

Good start, by when you take the derivative of your solution, it should yield the original function, but does not ....

d/dx {2/3 (4+cosx)^3/2} = {(4+cosx)^1/2}*{-sinx}

The last term comes about after taking the derivative of the (4+cosx)

Cheers,
Pete

User currently offlineJetService From United States of America, joined Feb 2000, 4798 posts, RR: 15
Reply 13, posted (10 years 6 months 2 days 22 hours ago) and read 443 times:

FOOLS!!! If you get 2.3x(cosx) by demihexing a quantified sinx then you get a multiplexed derivative. That's great if you want calculate the ground speed of an exploding turd. Try sampling d+2/3 by the square root of d/dx and you'll have the cos of the reverse tangent which is 17 parsed out to sequential quantity. JEEEEE-zus, I'm tired of doing your homework for you guys!!!!!!

By the way, I Like To Fly is right. The only math you'll need is making sure you get the right change after you buy that computer.


"Shaddap you!"
User currently offlineILS From , joined Dec 1969, posts, RR:
Reply 14, posted (10 years 6 months 2 days 22 hours ago) and read 440 times:

Do it on your graphing calculator.

User currently offlineDelta-flyer From United States of America, joined Jul 2001, 2676 posts, RR: 9
Reply 15, posted (10 years 6 months 2 days 21 hours ago) and read 434 times:

By the way, I Like To Fly is right. The only math you'll need is making sure you get the right change after you buy that computer.

You're right -- we taxpayers could save a lot of money cutting out all the useless education we give you young'uns. Just think how many computers I could have bought with the money I would have saved!

Cheers,
Pete

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