Find the antiderivative for a function Hi! I'm a little confused about a calculus exercise. Can som

g2esebyy7

g2esebyy7

Answered question

2022-05-01

Find the antiderivative for a function
Hi! I'm a little confused about a calculus exercise. Can someone please check if my logic is right?
The task: Find the antiderivative for a function f if f is a continuous function and if F ( x ) = f ( x ) for all real numbers x, of 1 4 f ( 2 x ) d x .
As far as I understand the answer is going to be 2 F ( 4 ) 2 F ( 1 )?

Answer & Explanation

Derick Alvarado

Derick Alvarado

Beginner2022-05-02Added 10 answers

Step 1
There is no "the" antiderivative of a function f. If F is an antiderivative of f, then so is F + C for any constant C.
The fundamental theorem of calculus tells you that if F is an antiderivative of f, then p q f ( x ) d x = F ( q ) F ( p )
Step 2
But now you have a b f ( 2 x ) d x. By a change of variable (1) a b f ( 2 x ) d x = 1 2 2 a 2 b f ( u ) d u
You can now apply the fundamental theorem of calculus to the right-hand side of (1).
For your problem, a = 1, b = 4.

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