Use the Second Fundamental Theorem of Calculus to find F'(x). F(x)=int_1^x (t^2)/(t^2+1)dt

nageljnovs6x

nageljnovs6x

Answered question

2022-12-19

Use the Second Fundamental Theorem of Calculus to find F'(x).
F ( x ) = 1 x t 2 t 2 + 1 d t

Answer & Explanation

Smeawnswelapno

Smeawnswelapno

Beginner2022-12-20Added 4 answers

If F is primitive of t 2 t 2 + 1 ,then by Fundamantal theorem for integral calculus,
1 x t 2 t 2 + 1 d t = F ( x ) F ( 1 ) d d x ( 1 x t 2 t 2 + 1 d t ) = d d x ( F ( x ) F ( 1 ) ) = F ( x ) 0 = x 2 x 2 + 1

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