Integrat - e

Calculus Level 1

Evaluate the value of

∫ 1 e 1 t d t \displaystyle \int_1^{\mathrm{e}} \frac {1}{t} \mathrm{d}t


The answer is 1.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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4 solutions

Daniel Liu
Jun 6, 2014

We see that ∫ 1 t d t = ln ⁡ ∣ t ∣ \displaystyle\int\dfrac{1}{t}\text{ d}t=\ln |t|

Thus the answer is simply ln ⁡ e − ln ⁡ 1 = 1 \ln e-\ln 1=\boxed{1} .

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Simple. :D

Sharky Kesa - 7 years ago

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yep.Rating 600 Calculus I bet, lol.

Daniel Liu - 7 years ago

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I have been busy with half-yearlies so didn't have much time to think of problems.

Sharky Kesa - 7 years ago

BTW, why do you think it doesn't have a rating? It doesn't deserve one.

Sharky Kesa - 7 years ago
Moniqua Brown
Aug 14, 2015

I put no thought into this

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Sophie Crane
Oct 31, 2014

This is one of the possible definitions of e e

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Shivam Vijay
Jun 6, 2014

Very esy.. integration of 1/t is logt And limit e gives log(e)=1 And limit 1 gives log(1)=0 So 1-0=1

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