Definite integral question

• Feb 11th 2007, 09:13 PM
Nick744
Definite integral question
Hey,

This is the question I can't get out!

For reference, the answer is 0.0126

Heres the question: Evaluate.

Attachment 1705

Nick
• Feb 12th 2007, 04:06 AM
topsquark
Quote:

Originally Posted by Nick744
Hey,

This is the question I can't get out!

For reference, the answer is 0.0126

Heres the question: Evaluate.

Attachment 1705

Nick

The integrand simplifies to 1/(3x^3) + 1/(3x^4) + 1/x^5, so the integral of this is -1/(6x^2) - 1/(9x^3) - 1/(4x^4). Putting in the limits gives:
[-1/(6*4^2) - 1/(9*4^3) - 1/(4*4^4)] - [-1/(6*3^2) - 1/(9*3^3) - 1/(4*3^4)] = 3133/248832 ( = 0.012591)

-Dan
• Feb 12th 2007, 11:31 AM
Nick744
Thanks heaps topsquark!

I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.
• Feb 12th 2007, 12:47 PM
topsquark
Quote:

Originally Posted by Nick744
Thanks heaps topsquark!

I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.

(Chuckles) But the power DOES increase. -2 > -3 for example. The power rule still applies even though the exponent is negative:
Int(1/x^n dx) = Int(x^{-n} dx ) = [1/(-n + 1)]*x^{-n + 1} + C

-Dan
• Feb 12th 2007, 07:55 PM
Nick744
Sorry, I don't know what I was thinking...stupid.

Please make out like this thread never existed.:rolleyes:
• Feb 13th 2007, 05:30 AM
topsquark
Quote:

Originally Posted by Nick744
Sorry, I don't know what I was thinking...stupid.

Please make out like this thread never existed.:rolleyes:

Don't think of it as "stupid." You are now more aware of this property, so your mistake had a use. It is better to ask the question than to not ask it.

-Dan