Asked by kieran
need some help im doin antiderivatives it has (2-x^2)^4xdx i understand how to do it for the most part but i come up with 1/5(2-x^2)^5+c the book has a answer of -1/10(2-x^2)^5+c how what am i doing wrong
Answers
Answered by
Steve
You may have forgotten a factor of -2:
∫(2-x^2)^4 x dx
if u = (2-x^2), du = -2x dx, so the integral is
∫u^4 (-1/2) du
= 1/5 (2-x^2)^5 (-1/2) + c
because you started out with x dx, but needed -2x dx to get du.
∫(2-x^2)^4 x dx
if u = (2-x^2), du = -2x dx, so the integral is
∫u^4 (-1/2) du
= 1/5 (2-x^2)^5 (-1/2) + c
because you started out with x dx, but needed -2x dx to get du.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.