# Integration Problem

## Homework Statement

I'm just having a bit of trouble with where to start on this integral.

$$\int[1 - (r/0.11)]^1^/^5rdr$$

## The Attempt at a Solution

I've tried using integration by parts, "u" substitution and things like that but I dont seem to be getting anywhere with this. Any help would be greatly appreciated.

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Gib Z
Homework Helper
Which substitutions did you try? Its obvious the stuff under the radical is giving you trouble, so why not try substituting it away.

The first substitution that comes to mind is to let u = (1-(r/0.11)) so du = -1/0.11 dr. Rearranging for dr I get dr = -0.11du. If I sub this into the integral I still have an r in the equation.

From here I rearranged the expression u = (1-(r/0.11)) for r to get r = (1-u)(0.11). If I sub this into the integral I get

I = $$\int(u)^1^/^5(1-u)(0.11)(-0.11)du$$
= $$\int(u)^1^/^5(1-u)(-0.0121)du$$

It looks a bit better than before but I'm still stumped, hopefully the work I've done up to here is correct.

Gib Z
Homework Helper
It is correct. Now just take the constant outside, and expand the brackets.

If I do that then the integral becomes

I = -0.0121$$\int (u^1^/^5 - u^6^/^5)$$
= -(0.0121)[(5/6)u6/5 - (5/11)u11/5]

So in order to get a solution I would also need to change the initial limits of integration using u = (1-(r/0.11)). If my initial limits of integration were 0 to 0.11 after subbing them into the equation for u my new limits of integration are from 1 to 0.

Gib Z
Homework Helper
Yes that is correct. If you want to follow convention you'll have to introduce a negative factor and swap the new limits of integration to ensure the upper limit of integration is larger than the lower limit of integration.