Undergrad Train Wreck Integral Shortcut...

[aronclark1017]

TL;DR

A tempting shortcut in long paths that leads to certain train wreck

Although this case is seemingly reasonable.
I(1,2) x^3 dx
[x^4/4](1,2)
[x^2](1,2)[x^2/4](1,2)=9/4

I(1,2) x^3 dx
[x^4/4](1,2)=15/4

 

[Ibix]

It helps if you use LaTeX. Is your question that if $$\int_1^2x^3dx=\left[\frac{x^4}4\right]_1^2$$then why is $$\left[\frac{x^4}4\right]_1^2\neq\left[x^2\right]_1^2\left[\frac{x^2}4\right]_1^2$$Because if so, write out the square brackets explicitly and you'll see why.

 

[Hill]

$(ab)|_1^2\neq a|_1^2\,b|_1^2$