Can You Cancel The Integral?

Calculus Level 1

True or false :

Given that ∫ 0 1 f ( x ) d x = ∫ 0 1 g ( x ) d x = 0 \displaystyle \int_0^1 f(x) \, dx = \int_0^1 g(x) \, dx = 0 , does it imply that f ( x ) = g ( x ) f(x) = g(x) for all x x ?

Yes No

View wiki
Abdalrahman Gamal by Abdalrahman Gamal , 26, Egypt

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Abdalrahman Gamal
Apr 11, 2016

No, a simple solution is to substitute f ( x ) = sin ⁡ 2 π . x and g ( x ) = cos ⁡ 2 π . x f(x) = \sin2\pi.x \text{ and }g(x) = \cos2\pi.x

5 Helpful 0 Interesting 0 Brilliant 0 Confused

A better argument would be to say that, the integral is equal only in the given period and it doesn't mean that it follows the same throughout the domain of the two functions. Anyways, good question, keep posting!

Sravanth C. - 5 years, 2 months ago

Good question. Try this problem that was inspired by you.

Calvin Lin Staff - 5 years, 2 months ago

Can you add an argument without example? My solution would be: "Area under the curve are equal. Hence it need not be necessary for f(x) to be equal to g(x)."

Aditya Kumar - 5 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...