Q8

Submitted by Anonymous (not verified) on

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Hi,
I'm just going Q8 and you have to make use of the fact that if you differentiate the integral of f(x) from 0 to t you get f(t)...
I've never come across this before... Why is this?

Help appreciated :)

Thanks

If you let F(x) be the

Submitted by hunter2 (not verified) on

If you let F(x) be the integral of f(x).

$\int^t_0 f(x) dx = F(t) - F(0) $

So,

$\frac{d}{dx}(\int^t_0 f(x) dx) = \frac{d}{dt} (F(t) - F(0)) $

$\Rightarrow \frac{d}{dx}(\int^t_0 f(x) dx) = f(t) $

Since F(0) is a constant.

Differentiation is meant to

Submitted by hunter2 (not verified) on

Differentiation is meant to be with respect to t on both sides

Thanks!

Submitted by fairydust2 (not verified) on

Thanks a lot, that makes sense :)