Antiderivatives I have this definite integral and I need to find its derivative with respect to t.

Leon Robinson

Leon Robinson

Answered question

2022-04-07

Antiderivatives
I have this definite integral and I need to find its derivative with respect to t. I am not sure how to do it without computing the value of the integral and taking its derivative.
2 t u 4 16 d u

Answer & Explanation

empatteMattmkezo

empatteMattmkezo

Beginner2022-04-08Added 22 answers

Explanation:
Note that in general
f ( t ) = a ( t ) b ( t ) g ( u ) d u f ( t ) = g ( b ( t ) ) b ( t ) g ( a ( t ) ) a ( t )
Carley Haley

Carley Haley

Beginner2022-04-09Added 3 answers

Explanation:
Apply Fundamental theorem of Calculus here. Let's define
f ( t ) = 0 t u 4 16 d u ..
Then f ( t ) = t 4 16

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