From the Fun Fact files, here is a Random Fun Fact, at the Easy level: One Equals Zero: Integral Form
Consider the following integral:
INTEGRAL (1/x) dx
Perform integration by parts: let
u = 1/x , dv = dx
du = 1/x^{2} dx , v = x
Then obtain:
INTEGRAL (1/x) dx = (1/x)*x  INTEGRAL x (1/x^{2}) dx
= 1 + INTEGRAL (1/x) dx
which implies that 0 = 1.
What's wrong with this calculation?
The Math Behind the Fact:
This is common mistake using integration by parts in calculus.
Students often forget about the constant of integration
for indefinite integrals. In this case, the constants
on both sides will differ by 1.
How to Cite this Page:
Su, Francis E., et al. "One Equals Zero: Integral Form."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
The Link for this Fun Fact:
is directly accessible here.
