- #1

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Now, I realize that you're supposed to use the fundamental theorem of calculus, and that it somehow works out that, for example:

[tex]

d/dx\int_{a}^{x} 2t dt = 2x

[/tex]

But when I do this, I actually do the integration then do the differentiation... I guess I'm not confident that just replacing t with x (in the example I gave) will work in general, like on a really bad integral like:

[tex]

d/dx\int_{a}^{x} \sqrt{1+t^3}

[/tex]

Does it really equal [tex] \sqrt{1+x^3} [/tex]??? I can't actually expand it out to see for sure...

Does this question of mine even make sense or am I crazy? Thanks!