Integrating sqrt(1+4x^2) from x = 0 to x = 1: A Step-by-Step Solution

[applestrudle]

Homework Statement

Integrate sqrt(1+4x^2)

limits x = 0 to x = 1

Homework Equations

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!

 

[Dick]

Homework Statement

Integrate sqrt(1+4x^2)

limits x = 0 to x = 1

Homework Equations

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!

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?

 

[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?

 

[applestrudle]

what a silly mistake, i feel embarrassed :S

 

[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.