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Roland Manning

Roland Manning

Answered question

2022-07-01

Antiderivative of 8 t 1 / 2
I am trying to find the antiderivative of 8 t 1 / 2 but im just not understanding how to do this.
I saw someone get out of t 1 / 2 the answer 2 t 1 / 2 . Can someone help me out?

Answer & Explanation

Trey Ross

Trey Ross

Beginner2022-07-02Added 30 answers

Step 1
Don't be worried about a negative exponent that's not -1: you apply the same rules as you would when integrating, say, 8 t 3 d t , , for example.
Those rules, recall, are:
Step 2
For any n 1 and any number b,
b x n d x = b x n d x = b 1 ( n + 1 ) x ( n + 1 ) + C (where  C  is a constant) .
So, since ( 1 / 2 ) 1 , 8 t 1 / 2 d t = 8 ( 1 2 ) t ( 1 2 ) + 1 ) + C = ?
Sonia Gay

Sonia Gay

Beginner2022-07-03Added 7 answers

Explanation:
x α d x = 1 α + 1 x α + 1 + C, as long as α 1. Also, note that 8 t 1 2 d t = 8 t 1 2 d t.

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