1. ## Integrals

Whats the difference between dt and dx?

F(X) = e^x + ∫ sin t dt

F(X) = e^x + ∫ sin t dx

Then calculate F(π)

∫ is 1 and x.

Somebody who can explain this kind of integrals shortly? why dt and not dx?

2. ## Re: Integrals

$t$ is just a dummy variable.

Fundamental theorem of calculus ...

$\frac{d}{dx} \left[\int_a^x f(t) \, dt \right] = f(x)$

3. ## Re: Integrals

ok, so if i understand you correct

∫ sin t dt <=> ∫ sin x dx

its just an other way to whrite it?

4. ## Re: Integrals

Originally Posted by ronaldopeter
Whats the difference between dt and dx?

F(X) = e^x + ∫ sin t dt

F(X) = e^x + ∫ sin t dx

Then calculate F(π)

∫ is 1 and x.

Somebody who can explain this kind of integrals shortly? why dt and not dx?
were these meant to be different functions, F(x) ?