if-2x-3-2-a-x-f-t-dt-then-f-a-

Question Number 134884 by abdullahquwatan last updated on 08/Mar/21

if {2 x}^{3} - 2 = \int_{a}^{x} f (t) dt, then f^{'} (a) = \dots

Answered by bemath last updated on 08/Mar/21

\frac{d}{dx} [{2 x}^{3} - 2] = f (x)

\Rightarrow f (x) = {6 x}^{2}; f^{'} (x) = 12 x

\Rightarrow f^{'} (a) = 12 a

Commented by abdullahquwatan last updated on 08/Mar/21

thx sir

Commented by bemath last updated on 08/Mar/21

you put a = 1

Answered by Ñï= last updated on 08/Mar/21

f (x) = 6 x^{2}

f {(x)}^{'} = 12 x

\int_{a}^{x} f (t) d t = \int_{a}^{x} 6 x^{2} d x = 2 x^{3} - 2 a^{3} = 2 x^{3} - 2

\Rightarrow a^{3} = 1

\Rightarrow f {(a)}^{'} = e^{2 i k π / 3} (k = 0, 1, 2)

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