Help Solving Online Math Problem - Can You Spot the Error?

[Exeter909]

I have to solve this online problem for homework and was wondering if anyone could help me with it, i can find the answer by graphing and solving, but don't know how to explain the mistake...

http://www.dougshaw.com/findtheerror/FTEusub.html

thanks for the help

 

[AKG]

If you have an integral from a to b (in this case, -1 to 1), u has to be a 1-1 continuously differentiable function of x with non-zero derivative. That is, u has to be a function of x defined on all of [-1, 1]. It has to be 1-1, so u has to take on a different value for every x. u has to be continuous, differentiable (with respect to x, i.e. you can find du/dx), and du/dx has to be continuous. Moreover, du/dx can never be 0, otherwise dx = du/u', so and if u' is ever 0, then when you change your variables, the integrand will have 0 in the denominator at some point, which isn't allowed. Your u substitution fails about half of these criteria.

For one, it is not defined when x = 0. Second, 1/x⁴ = 1/(-x)⁴, so u repeats the value 1/2⁴ at both x = 1/2 and x = -1/2.

 

[Exeter909]

thank you

thank you!