Question

Problem Set 5 Incorrect Solution?

Answer 1

Can anyone verify that Integration Problem Set 5, problem 3A-2E provides an incorrect solution?
Using substitution where:
\[u = 8-2x^{2}, du = -4xdx\]

… the solution then goes on to assume \[\int\limits_{}^{-} xdx/\sqrt{8-2x^{2}} = \int\limits_{-}^{-}u^{1/2}(-1/4)du\]…
but shouldn't that be… a -1/2 power instead, resulting in:
\[=\int\limits_{-}^{-}u^{-1/2}(-1/4)du\]?

The final solution I get:
\[-2\sqrt{8-2x^{2}}\]

Answer 2

This is one of a number of problems for which I've noted errors in the solution. Somehow they've offered a solution for u^(1/2) rather than the problem that was actually posed, which is u^(-1/2). You may want to check your solution, though, shouldn't it be -1/2 out front?

Answer 3

Good to know! I'll take a look at your answer history before re-posting any questions :)
Also, you are right about my solution... I somehow thought -2/4 = -2 ha! The -1/2 out front looks better.
Thanks again Creeksider!