Watch this before your calculus 2 final! Top 4 integration mistakes students often make!

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This video covers the top common mistakes when doing integration. Hope this severs as a good review before your calculus 2 final!

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From a teacher’s perspective, A is a student who made a careless mistake. C seems like a student who either froze/ran out of time or just forgot and wrote the only formula they could remember. D knows the antiderivative of rational functions is associated with the natural log function, so they have the big picture but not the details.

B is pretty rough. Unless the student forgot several trig identities, this shows they either didn’t properly do a u-sub and/or don’t know the chain rule.

briangronberg

My question is: if you are the exam supervisor, would you allow students to wear that jumper in an exam?

jansentanu

Like a noob at the beginning I was like : "Wait, bring the 3 then minus 1... That was correct" before noticing an absent "+ C"

sxkjknjw

I was quite reasonable with integration problems in my youth, this has just reminded me how much I've forgotten through lack of use. 🙁

WideCuriosity

I have watched so many of your integral vids that I'm gonna be a master at integration when I take it next month😅

bahaagamer

Half angle double angle identifies are practically part of my soul now. Trig subs were the most fun to integrate. So many triangles drawn.

Taterzz

I knew why all these were wrong from the thumbnail and I just finished Calc IV why am I here

JosaxJaz

Love this. I like the question "Which is worst?"

DrRBERT

I’m literally written tomorrow😂
Thanks a lot

stefanduplessis

I’d say A is the worst because it doesn’t even have +c

Brid

2:11 you can use reverse power rule for (x+a)^n where a is a real number, not just for a=0

justinpark

Here is another one: Anti derivative of lnx is 1/x. I see this mistake a lot in Integration by parts where lnx is the g'. For example an integral like x^5*lnx...Calculus 2! If a student only forgot +C, well that is still something I can live with...kind of...

mathisnotforthefaintofheart

I learnt how to change sin^2x and cos^2x into cos(2x) from
cos(2x)=2cos^2(x)-1
So I would argue that in B you could actually use sin^2(x)=1-cos^2(x)
And substitute cos^2(x)=(cos(2x)+1)/2

samsonpl

In my honest opinion, C is the worst mistake.

Missing the constant of integration is forgivable because they at the very least did the bulk of the computation correctly.

B is the second worst because they forgot chain rule but, it pales in comparison to C where they literally forget the concept of derivative and integral all together and mismatch them.

Forgetting the chain rule is one thing because you at least still know the other rules but, forgetting the difference between integral and derivative is a whole new level of stupidity from that.

D is more forgivable because I see someone getting tripped up by that easily (at least early on) because, it looks so similar to something completely different that they would be tempted to say it even if it’s far off. It shows they at the very least can differentiate between integral and derivative and can do other types of integrals correctly which is better than B and C but still worse than A because with A the whole computation was correct it was just they forgot the plus C.

CalculusIsFun