Short question about integrals

[jet10]

integral identity

if we have $$\int dt f(t) = \int dt g(t)$$ where both integrals are indefinite integrals, can we immediately conclude that f(t) = g(t) ? I know this doesn't work with definite integrals.

 

[vsage]

If the two integrals are equivalent, then this implies to me at every t the shapes of f(t) and g(t) are equivalent. It does not work with definite integrals because it's entirely possible for two functions to have the same integral over a certain interval but have entirely different shapes.

 

[CarlB]

Write it out in complete for example:

$$\int^xdt\;f(t) = \int^x dt\;g(t).$$

In other words, write the indefinite integrals as definite integrals. Now apply the fundamental theorem of calculus and you will find out that yes, indeed, f = g.

Carl

 

[jet10]

thanks! carl