Question

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

Answer 1

\[h(x) =\int \limits_{-6}^{\sin x} (\cos(t^7)+t) dt\]


\[\implies h'(x) = \dfrac{d}{dx}\int \limits_{-6}^{\sin x} (\cos(t^7)+t) dt\]

Answer 2

\[\implies h'(x) = \dfrac{d}{dx}(f(\sin x) - f(-6)) dt\]

\[\implies h'(x) = f'(\sin x)(\sin x)' - 0\]

\[\implies h'(x) =(\cos(\sin^7 x) + \sin x)(\cos x) \]

Answer 3

last line is by FTC1,
second last line is by chain rule

Answer 4

let me knw if smthng doesnt make sense..

Answer 5

I will

Answer 6

for h'(x)=f'(sin(x)(sin(x))'-0

the (sin(x))' becomes the cos(x)

i forgot the last bit. that's why i kept getting the wrong answer

Answer 7

@ganeshie8

Answer 8

yes... was there a question ? :)