# Derivative of definate intagral / second derivative? idk.

• Jan 7th 2009, 02:54 PM
ifeustel
Derivative of definate intagral / second derivative? idk.
find
(d/dx) ((2)S(x^2)) ((t^3) – 1) dt i.e. derivative of the intagral from 2 to xsquared of t cubed minus one in relation to t

then find F^II (second derivavtive of F)

I know capital F means something different than lower case f, but does it matter in this case? I think this problem is a lot easier than I think it is. Help please?
• Jan 7th 2009, 02:59 PM
Mush
Quote:

Originally Posted by ifeustel
find
(d/dx) ((2)S(x^2)) ((t^3) – 1) dt i.e. derivative of the intagral from 2 to xsquared of t cubed minus one in relation to t

then find F^II (second derivavtive of F)

I know capital F means something different than lower case f, but does it matter in this case? I think this problem is a lot easier than I think it is. Help please?

$f'(x) = \frac{d}{dx} \int_{2}^{x^2} t^3-1 dt$

$f'(x) = \frac{d}{dx} [\frac{1}{4}t^4-t]_{2}^{x^2}$

$f'(x) = \frac{d}{dx} [\frac{1}{4}(x^2)^4-x^2-\frac{1}{4}(2)^4 + 2]$

$f'(x) = \frac{d}{dx} [\frac{1}{4}x^8-x^2- 2]$

Better?

Usually in such a context, the notation [/tex] F'(x) = f(x) [/tex] and hence $F''(x) = f'(x)$, which is what you just worked out above ^. But perhaps they mean they want you to find $f''(x)$, in which case you would integrate your answer above again.