Can you integrate this in 60 seconds? #calculus

[HenkVanLeeuwen-io]

I took longer than 60 s but I found 2A=1.

[jaskiraatshah]

integrate: ln(x-1)/(x-1)__>first let u=ln(x-1)
du = dx/(X-1) hence integrate wrt u
integrate: u du which is u^2/2 whereas the range is between 1 to 0 in terms of u
replace 1 with u and you'll achieve "1/2" and with zero you get zero, subtract real quick and you still get 1/2 as A
then multiply by 2
and there you go

[Kaviranghari]

It took me 30 seconds to figure out substitution method and 20 to get 1😊

[probaye]

ln(1 - 1/x) = ln((x-1)/x) = ln(x-1) - ln(x). ln(x) cancel so the integral simplifies to ln(x - 1)/(x - 1) dx from x = 2 to x = e + 1. In the u world this is u du from u = ln (1) = 0 to u = ln (e) = 1. This is a triangle with area 1/2, so 2A is 1.

really cool problem took me a few minutes :D

[nvapisces]

How does so many people get answer of 1 when I got 2? I solved the integral to get A=1, then 2A=2

[Hemshankar]

It takes me 5 minutes to understand but did it in 45 second 😅😅😅

[sylveonimran]

i just finished algebra one what os this 😭

[RM-levb]

Did it under 15 sec without any paper or som’ i’d say;jokes to a physicist!

[m.ewart]

Here's my take at this one:

1) Distribute the ln to reach
A = the integral from 2 to e+1 of ln(x-1)/(x-1) dx

2) Use the substitution u = x - 1 (du = dx) so A = the integral of ln(u)/u du from 1 to e

3) Writing f(x) = ln(x) the integral to be evaluated is of the form f(u) × f'(u) du, so integration by parts yields:
A = ( (ln(e))² - (ln(1))² ) - A
<=> 2A = (ln(e))² - 0

Therefore, 2A = 1.

[truthiz]

These kids solve problems like this while I could not figured the tip for my waitress

[Just_H_]

It's so easy that i can solve this in 10 seconds without using pen

[RazzaQ_Ansari]

A = -3/2 & 2A = -3. And guess what I did it without using pen and paper. It is very basic for us indians 🇮🇳🤦‍♂️

[Superman]

Who else solved for A to be 1/2 before seeing the question asked for 2A?

[j]

i just randomly guess a number, could be 1

[champu]

Answer is 1

I fr did this in 60 sec which i didn't expect 💀

[xa--animesh]

Bruh this is 10 second question u can do it in mouth

[prithvisinghpanwar]

it took me 0.01 seconds to find the answer 2A=1😊














just by tapping once

[georgejosiah]

I got the ans in less time only because i quess it was a trick question whose ans is between 0 - 2.