- #1

- 24

- 0

Mod note: Edited the LaTeX so that the exponents show up correctly.

This is from my Calculus II exam practice papers. We're currently dealing with different substitution methods (whichever apply to the given problem).

[itex]

\int \frac {\sqrt{1 - x^2}} {x^{4}} dx

[/itex]

So I started off by attempting to rewrite it as:

[itex]

\int (1 - x^2)^\frac {1}{2} (x^{-4}) dx

[/itex]

So, let: [itex]u = x^2[/itex] and [itex]du = 2x dx[/itex]

Rewriting formula again:

[itex]

\int (1 - u)^\frac {1}{2} (u^{-2}) du

[/itex]

Integrating.....

[itex] \frac {-2}{3} (1 - u)^\frac {3}{2} (\frac {u^{-1}}{-1}) + constant [/itex]

Subbing the U out and fixing things up a bit....

[itex]

\frac {2}{3}(1 - x^2)^\frac {3}{2} (\frac {1}{x^2}) + constant

[/itex]

Quite frankly, I am honestly not sure if I am doing this correctly so far. This is actually the third process I've tried (the first 2 were even longer). I'd like to be shed some light if I am going about this correctly or not. Thanks in advance.

PS: I posted (part 1) on the topic since I will require assistance in a few other examples in this paper. Should I keep posting my questions regarding the other problems in this same thread or a new one?

## Homework Statement

This is from my Calculus II exam practice papers. We're currently dealing with different substitution methods (whichever apply to the given problem).

## Homework Equations

[itex]

\int \frac {\sqrt{1 - x^2}} {x^{4}} dx

[/itex]

## The Attempt at a Solution

So I started off by attempting to rewrite it as:

[itex]

\int (1 - x^2)^\frac {1}{2} (x^{-4}) dx

[/itex]

So, let: [itex]u = x^2[/itex] and [itex]du = 2x dx[/itex]

Rewriting formula again:

[itex]

\int (1 - u)^\frac {1}{2} (u^{-2}) du

[/itex]

Integrating.....

[itex] \frac {-2}{3} (1 - u)^\frac {3}{2} (\frac {u^{-1}}{-1}) + constant [/itex]

Subbing the U out and fixing things up a bit....

[itex]

\frac {2}{3}(1 - x^2)^\frac {3}{2} (\frac {1}{x^2}) + constant

[/itex]

Quite frankly, I am honestly not sure if I am doing this correctly so far. This is actually the third process I've tried (the first 2 were even longer). I'd like to be shed some light if I am going about this correctly or not. Thanks in advance.

PS: I posted (part 1) on the topic since I will require assistance in a few other examples in this paper. Should I keep posting my questions regarding the other problems in this same thread or a new one?

Last edited: