Turn in #9 is due Monday, Dec. 8, 2014!
This is for discussing assignments from WEEK 1, including homework,
turn-in #9, and in-class work or lessons, or anything else related to the
class from this week. Please be sure to include your
name at the end of your post for credit. When answering a question, DO
NOT GIVE SOLUTIONS! Provide hints or explain a method that you used, but
do not give the final result. As always, RESPECT IS A MUST! Anyone
abusing this forum will be banned from future use (meaning, no extra
credit!!!).
When should we use a table when using the integration by parts formula?
ReplyDeleteThanks,
Rachel Hersch
If I recall correctly, Mr Wilson mentioned that using a table will simplify the work required to evaluate the integral and is particularly useful when evaluating the integral requires multiple usages of the IBP.
DeleteRafey Rehman
You may omit question 4d (part d of question 4) on turn in 9.
ReplyDeleteFor 1b, should we treat it as an indefinite integral?
ReplyDeleteSarah Fried
Yes, but as it asks you to find "an" antiderivative (meaning any antiderivative) you don't even need to add the +C.
DeleteI wasn't sure how to approach problems like #5 on Techniques for Integration #2. I found something online saying that in the situation where we have a +bx^2, to substitute (the square root of a / the square root of b)u for x. Is this a good approach, and why does it work? Thanks,
ReplyDelete-Safia Sayed
Try factoring 4 out of the denominator, so you have (1 + (9x/4)). This, then is just the derivative of arctan(3x/2)! The "trick" you refer to is called a trig substitution, which is essentially the above process, just a bit more cumbersome.
DeleteAre there any cases where there isn't any component of LIPET but you still have to integrate by parts? If so how would you know what to set equal to u and dv?
ReplyDeleteThanks,
Rachel Hersch
None come to mind.
DeleteOn the turn in for 1a and 1c, should the initial time value in the integral be 0 or 1 since it gives you the volume of the lake at t=1?
ReplyDeleteThe initial time value should be 1 since we have to find how much water is pumped out of the lake from the value of 60,000m^3 which occurs at t=1.
Delete-Allison Honet
Is there a way to know by looking at a problem whether or not you have to you use substitution or integration by parts?
ReplyDeleteThanks,
Lexi Kizy
Substitution is used when we have a composition of functions (undoing chain rule), while IBP is used when we are integrating a product of functions. IBP also works, however, to integrate some functions that would not otherwise be possible (such as ln or arctan).
DeleteAre there any important integrals we should just have memorized?
ReplyDeleteThanks!
Laura Goo
Any derivative rule that I recommended you memorize is also an anti derivative rule. Some key ones, as Rafey points out, are the inverse trig functions. Arctan will show up more and more frequently as we progress through the course (you will be quite surprised actually at how often it appears!).
DeleteYou should definitely memorize the inverse trig functions anti-derivatives.
ReplyDeleteRafey Rehman
Are the answers to the worksheets done in class on Thursday and Friday online?
ReplyDelete-Amanda Bachand
Yes, the HW answers are. The in class work is not as we went over them in class.
Deletewhen do we know when to add +c to an integral of an equation? Do we add +c all the time or just when the question asks for the integral, not a singular integral of the equation? Thank you!
ReplyDelete- Maggie Hammond
We ALWAYS need "+C" for an indefinite integral!
DeleteWill the new material we learned today be on the quiz tomorrow?
ReplyDelete-Julia T
No.
Delete