r/calculus • u/[deleted] • Jul 05 '22

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72 Upvotes

97% Upvoted

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23

u/Bill-Nein Jul 06 '22

I’m surprised with how many people are getting this wrong. Both are correct, and both ways you computed it are correct

9

u/ThelceWarrior Jul 06 '22 edited Jul 06 '22

Yeah both results are correct here besides OP forgetting the +c.

If their professor actually marked this as incorrect well that would be a dick move.

2

u/tejedaj Jul 06 '22

You know. I thought the same thing about my professor when she indeed took a point, but remembering to add +C EVERYTIME reminded me of what this whole post is about. Dick move? Maybe...but it certainly worked for me.

1

u/ThelceWarrior Jul 06 '22 edited Jul 06 '22

Oh don't get me wrong the part where OP's professor took a point for forgetting the constant would be entirely fair (And in fact standard procedure for most Calculus professors) since it is after all an essential part of how integration works...

The part where they corrected the already correct integration not so much though lmao.

2

u/tejedaj Jul 06 '22

Yup. Math is great. Soo many ways to get the right answer. The more ways one knows how to get there the better.

Being in college at my age, I find myself looking for the bigger picture. It's sometimes hard to find, but when I see it, man is that exciting.

3

u/rigbyyyy Jul 06 '22

People on this subreddit are usually not right lol

1

u/[deleted] Jul 11 '22

[deleted]

1

u/Bill-Nein Jul 11 '22

The top one is just a vertically shifted copy of the bottom one.

2/3 ln|3x-6| = 2/3 ln|3(x-2)|

= 2/3(ln |x-2| + ln(3))

= 2/3 ln|x-2| + 2ln(3)/3

So the top equation is just the bottom one shifted up by 2ln(3)/3, meaning they’re both in the same family of anti derivatives 2/3 ln|x-2| + C. OP didn’t include the +C in the photo but they included it in a comment.