Question

fundamental theorem of calc part I question WILL GIVE 2 MEDALS!! (:

Answer 1

2 medals ? XD how is that possible?

Answer 2

watch

Answer 3

\[f(x) = \int \limits_x^{x^2}5\sin^2t dt\]

\[\implies f'(x) = \dfrac{d}{dx}\int \limits_x^{x^2}5\sin^2t dt\]

\[ ~~~~~~~~ = \dfrac{d}{dx}[f(x^2) - f(x)]\]

\[ ~~~~~~~~ = f'(x^2)(x^2)' - f'(x)(x)'\]

\[ ~~~~~~~~ = 5\sin^2(x^2)(2x) -5\sin^2(x)(1)\]

Answer 4

see if that makes sense...

Answer 5

ok ill study thanks!

Answer 6

last line is by FTC
second line from last is by chain rule

Answer 7

essentially its FTC1+chainrule