Find the antiderivative of sqrt{3x-1}dx

comAttitRize8

comAttitRize8

Answered question

2022-07-20

Find the antiderivative of 3 x 1 d x.
I got 2 3 ( 3 x 1 ) 3 / 2 + c but my book is saying 2 9 ( 3 x 1 ) 3 / 2 + c.
Can some one please tell me where the 2/9 comes from?

Answer & Explanation

Reese King

Reese King

Beginner2022-07-21Added 13 answers

Step 1
3 x 1   d x = ( 3 x 1 ) 1 / 2   d x
Let u = 3 x 1, d u = 3   d x, so
( 3 x 1 ) 1 / 2   d x = 1 3 u 1 / 2   d u
Add one to the power of u, and divide by the new power
3 x 1   d x = 1 3 u 1 / 2   d u = 1 / 3 3 / 2 u 3 / 2 + c = 2 9 ( 3 x 1 ) 3 / 2 + c
Step 2
Your problem is that you need to take into consideration the derivative of Your problem is that you need to take into consideration the derivative of 3 x 1, which means you need to divide by 3, giving you the factor of 1 3 missing from your answer.
As was suggested in the comments of your previous question, if you differentiate the answer that you got with the chain rule, then you'll see why you've made a mistake
d d x ( 2 3 ( 3 x 1 ) 3 / 2 ) = 3 2 2 3 ( 3 x 1 ) 1 / 2 d d x ( 3 x 1 ) = 3 = 3 3 x 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?