How do you use the second fundamental theorem of Calculus to find the derivative of given $int sqrt((t^3)+1)$ from $[-1, x]$ ?

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Answer 1 · 2016-08-10T16:22:30

$sqrt((x^3)+1)$

FTC part 1 tells us that

$d/dx( int_a^x f(t) dt )= f(x)$

so $d/dx( int_(-1)^x sqrt((t^3)+1) dt )$

$sqrt((x^3)+1)$

How do you use the second fundamental theorem of Calculus to find the derivative of given int sqrt((t^3)+1)int sqrt((t^3)+1) from [-1, x][-1, x]?