# Integrate sqrt(1+4x^2)

1. Jan 21, 2014

### applestrudle

1. The problem statement, all variables and given/known data

Integrate sqrt(1+4x^2)

limits x = 0 to x = 1

2. Relevant equations

3. The attempt at a solution

let 2x = sinhu

I = 0.5 ∫ (coshu)^2du

limits u = 0 u = sinh^-1(2)

0.5 ∫ (e^2u +e^-2u +2)/4 du

0.5 [(e^2u)/8 -(e^-2u)/8 +2u]

I = 2.56 which is wrong :(

why is it wrong?

please help!

Last edited: Jan 21, 2014
2. Jan 21, 2014

### Dick

Well, for one thing 0.5 ∫ (e^2u +e^-2u +2)/4 du becomes
0.5 [(e^2u)/8 -(e^-2u)/8 +u/2]. Did you forget to divide the last term by 4?

3. Jan 21, 2014

### brmath

You started out well. I think you made an arithmetic mistake when you multiplied your expression through by .5 -- you got $e^{2u}/8 + e^{-2u}/8 +2u$. Where did you get 2u. Shouldn't it be u/4?

4. Jan 23, 2014

### applestrudle

what a silly mistake, i feel embarrassed :S

5. Jan 23, 2014

### brmath

I recently wrote that 25 is divisible by 3. And just a few months ago based a proof on the non-fact that 10 is prime. Talk about embarrassed. Losing a factor of 4 is much more understandable.

We cannot escape these boneheaded errors.

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