# Math Help - integration

1. ## integration

need some help

if f(x) = x^2
t^2dt
x

then

f'(x)=
f'(1)=

2. Is that supposed to be $f(x)=\int_{x}^{x^{2}}t^{2}dt$?.

If so, $\frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)$

3. Originally Posted by dat1611
need some help

if f(x) = x^2
t^2dt
x

then

f'(x)=
f'(1)=

If $f(x) = \int_x^{x^2}{t^2\,dt}$

what is $f'(x)$ and $f'(1)$?

If so... evaluate the integral...

$f(x) = \left[\frac{1}{3}t^3\right]_x^{x^2}$

$= \frac{1}{3}(x^2)^3 - \frac{1}{3}x^3$

$= \frac{1}{3}x^6 - \frac{1}{3}x^3$.

Now take the derivative...

$f'(x) = 2x^5 - x^2$.

Now let $x = 1$

$f'(1) = 2\cdot 1^5 - 1^2$

$= 1$.

4. What about if you can't explicitly compute its primitive?