What my calculus 2 students did to this integral!

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bprp #shorts

[dvaVivy]

At least they didn't forget about the C

[KreiTech_StevenVieroPardosi]

this is why we have to be at least good at algebra before into calc

[Algebrainiac]

I died inside when I saw them cancelling out cos

[sajjadbagdadi]

That step ruined my day, an hour of silence for the Mathematics teacher correcting this

[mathevengers]

A great blunder which destroys mathematics and kills teachers.

[jamesvaughn]

Me who didn’t finish algebra: “doesn’t understand”
Also me: That idiot

[daniellancet]

What's 20 divided by 4?
Calc Students: *Fumbles for calculator*

[houseflyer]

ouch.
that hit me right in the feelings

[zapking]

That took me longer than I care to admit to realize what was wrong there

[nachiketkamble]

My first thought would be to rationalize and then see for substitution.

[technologyios]

Actual answer : sin^-1(x)-tan(sin^-1(x)) +C

[AnjaliSingh-vwkg]

How you cancelled cosx, that is illegal

[bozrnvr]

when you forget of our lord euler and his postulates :(

[angelmendez-rivera]

At the step where the student had the integrand, cos(t)/[1 + cos(t), they should have tried multiplying the numerator and denominator by 1 – cos(t). This would have allowed them to obtain cos(t)·[1 – cos(t)]/[1 – cos(t)^2] = cos(t)·[1 – cos(t)]/sin(t)^2 = [cos(t) – cos(t)^2]/sin(t)^2 = [cos(t) – 1 + sin(t)^2]/sin(t)^2 = cos(t)/sin(t)^2 – 1/sin(t)^2 + 1 = cot(t)·csc(t) – csc(t)^2 + 1, and if the student knows their trigonometric derivatives, then they can antidifferentiate this very easily, obtaining cot(t) – csc(t) + t. Then they can substitute back x = sin(t), sqrt(1 – x^2) = cos(t), and they would obtain sqrt(1 – x^2)/x – 1/x + x = [sqrt(1 – x^2) – 1]/x + x. They can rationalize the numerator to simplify the answer, obtaining x – x/[1 + sqrt(1 – x^2)], and here, they can simply add the constant of integration to obtain the final answer x – x/[1 + sqrt(1 – x^2)] + C

[adamanimations]

when u forget u cant cancel out terms and factors without :

[SHAHID_NAUSHAD]

cosx/(1+cosx) = {cos²(x÷2) - sin²(x÷2)}/{2cos²(x÷2)} = 1/2 - tan²(x÷2) = and Finally Integral this problem ? = x/2 - 2sec²(x÷2) +x + C. Ans. 😊

[braydencraven]

A huge part of why students struggle with this is that when schools start teaching algebra, math becomes a game of memorizing a whole bunch of rules rather than learning how things actually work.

[christopherdavidson]

I haven't even set foot in Calc 2 and even I was like, "wtf is he doing?"

[JesusMartinez-zuxl]

Once I saw that dx for cosine I cried inside😅

[assassin]

Obviously the cancellation of the cos is wrong, but what would you do at this point?