Question

Help in calculus please.

Answer 1

@RaphaelFilgueiras

Answer 2

The questions are the attachments.

Answer 3

for the second one use Newton Leibnitz rule http://en.wikipedia.org/wiki/Leibniz_integral_rule..m not quite sure abt the first..

Answer 4

check the variable limits form..

Answer 5

How do you do that can someone show me

Answer 6

@Rea201 consider my approach:

\[ \large F(x)=\int_{2}^{x^2} \left( \frac{1}{t^2}\right)dt=F^*(x^2)-F^{*}(2)\]now differentiate it, ignore the middle term and work with the LHS and the RHS
\[F'(x)=\left( F^{*}(x^2)-F^{*}(2)\right)'=F^{*}(x)' 2x =2xf(x)\]

Answer 7

note: The notation in your question is very confusing, I recommend substituting without the loss of generality G(x)=F(x) and try to find G'(x) = g(x).

Answer 8

I get that thanks

Answer 9

ah you already had this one solved?

Answer 10

no I mean I understand your approach it makes a lot of sense

Answer 11

oh, even better than, great.