Integrate sin(4x)

[blike]

:pi:/2

:int: sin(4x)dx

0

 

 

:int: sin(ax)dx = -1/a cos(ax) right?

 

so

 

. . . . . . . . . :pi:/2

-1/4 cos(4x) |

. . . . . . . . . 0

 

[(-1/4) cos 4:pi:/2] - [-1/4(cos 4(0))]

 

(-1/4) - (-1/4)

 

0

 

?? where did I go wrong

[fafalone]

You didn't. 0 is the correct answer.

[Radical Edward]

sines and cosines are as much up as they are down, so an integral over infinity will always be zero.

[Dave]

For the graph y=sin(4x), over a range 0 -> 2*pi of x values, you can say that there are 4 ordinary sine curves, but they are all crammed together in the space where there would only be one. If you're going to take a quarter of this range, then clearly the area underneath this quarter is going to be equal to the area underneath one of these crammed sine curves, which will be zero.

[blike]

woo! I was sure that it couldn't have come out to 0. I plugged it into my ti83 and it gave a nonzero answer.

 

I left my answer as zero on the exam though, so I got it right

[fafalone]

That's what you get for using a TI-83, my TI-89 gave me zero.

[Dave]

same here.

[Tom Mattson]

Originally posted by blike

woo! I was sure that it couldn't have come out to 0. I plugged it into my ti83 and it gave a nonzero answer.

 

My guess: Your calculator was in "degree" mode, and you entered the limits of integration in radians.

 

Tom

[Bsun]

You shouldn't need calculators for Calc1,2, or 3...

[fafalone]

You need them if you're lazy and/or don't understand it. Personally I think taking calc 1 again is a waste of my time, so there's no reason not to do a hour long test in 5 minutes on my calc.

[Dave]

Originally posted by Bsun

You shouldn't need calculators for Calc1,2, or 3...

 

I rarely use my ti-89 apart from checking I have the right answers. In general, I don't really use a calculator at all apart from working out values for sin, sqrts, etc.

[blike]

Originally posted by Bsun

You shouldn't need calculators for Calc1,2, or 3...

 

For the most part, true. I used it mostly to check answers, but I'll admit I use it to do fractions quickly too

 

= sux at those

[JoeDaWolf]

Originally posted by Bsun

You shouldn't need calculators for Calc1,2, or 3...

 

there is a calculator portion on the ap test for calc 1 and 2. theoretically you don't need it, but if the problem calls for integral of (sin(x)^2 - cos(x)^3 dx) from 0.3 to 1.7...then u need it

 

~Wolf

 

P.S. I don't know if this goes on in other schools...but do all you TI-89 people think your sooo special? In my calc class, they think that they're god's gift to earth for having a machiene that produces variable integrals and derivitves

TI-83+ is good enuf for me

[blike]

Originally posted by JoeDaWolf

but do all you TI-89 people think your sooo special?

 

Special?? hardly! they compare themselves to God Himself.

 

I've been laughed at many times for my 83+

[JoeDaWolf]

AHAHAHA...expcet we ti-83 users have the last laugh...most of the peeps in my calc class have admitted that because of their 89s, they've forgotten how to do integrals easily (ap test thursday)...in all of my practice tests, i always try to do the integrals by hand.

[Dave]

Originally posted by JoeDaWolf

P.S. I don't know if this goes on in other schools...but do all you TI-89 people think your sooo special? In my calc class, they think that they're god's gift to earth for having a machiene that produces variable integrals and derivitves

TI-83+ is good enuf for me

 

Nope, but when I was shopping around for calculators for uni, I thought "what the hell, I may as well get the more expensive calculator because it does more". If you're going to fork out quite a bit for a ti-83, then you may as well go the whole way and fork out a little more for a ti-89.

 

Plus, it is a brilliant calculator. But it doesn't make you a lot better at maths.

[JoeDaWolf]

i got my ti-83+ before the ti-89 came out

[Dave]

Fair enough. I've found TI calculators to be superior to the other brands of calculator out there in a lot of ways, and they're very easy to program.