Thursday, February 17, 2011

Brevity is the soul of wit

I had the Calc II students tweeting again today, this time about the appropriate way to solve trig integrals involving sines and cosines. In 140 characters or less, how much can you say about solving such integrals? Below are some of the strongest responses. (By the way, "EFTI" means "Everyone's Favorite Trig Identity," my term for the identity sin2(θ) + cos2(θ) = 1.)

"If you see an odd # of cos(x), u=sin(x).If you see an odd # of sin(x), u=cos(x).If they are both even then throw your things and cry:("

"If there is an odd number of cos(x),letu=sin(x). If there is an odd number of sin(x) let u=cos(x).Then use trig identity if needed."

"To solve integrals with sin & cos, u=sinif ur cos is odd. u=cos if ur sin is odd. If both are even: weep. And Patrick spake it thus."

"Use EFTI!If the trigS has an odd and an even, make u=the even term.If the exponent is higher than 2,it may be easiest to seperate it first!"

"Integral with sin&cos: u sub the non-odd and sub the remainder with trig identity, then simplify. The rest should be easy."

"To solve intergral w/ sin & cos/if you see odd # of cos u=sin if you see odd # of sin u=cos/think of how to split them upsoit works out right"

"when u hav sine&cosine,ur u is the nonodd one.if both r odd u can choose either then use usub and EFTI to solve the trigintegral.its so fun!"

"In general: If the integral has an odd # of sins or cos, make the opposite one the u in the u-substitution set up.(Be careful of evens!)"

"Ifanodd#ofcos,u=sin(x)Ifanodd#ofsin,u=cos(x)Thendifferentiatetheu,andrememberthat1=sin2(x)+cos2(x).Settheintegralintermsofuandsolvewithrespecttou"

"If the powers are even/odd, use the even one as u. Iff there are extra of the odds, use EFTI. If both are odd, use the higher power as u."

I should mention that the overall quality of these tweets was stronger than that of the last set. Words were selected more carefully and fewer students felt the need to forgo spaces to say what they needed to in the room provided. I'm not sure if this improvement is a consequence of a more easily-summarized topic or a growing acquaintance with the genre. Maybe a little of both?