how do you antidifferentiate x^4 / 8
2007-06-14 07:54:31 · 5 answers · asked by Sarah M 1 in Science & Mathematics ➔ Mathematics
When you differentiate, you multiply by the exponent and then reduce the exponent by one. For example, when you differentiate x^3, you get 3x^2.
How do you reverse this? Well, you increase the exponent by one, and then divide by it. So 3x^2 becomes x^3.
For the problem you have: (1/8)*x^4 becomes (1/8)*(1/5)*x^5. That's x^5/40. Plus a constant of integration, C. That's because you have to account for the fact that any constant, when differentiated, goes away - so the antidifferentiated (or integrated) equation could've started out with any constant.
Answer: (1/40)*x^5 + C
Hope that helps!
2007-06-14 08:02:31 · answer #1 · answered by Bramblyspam 7 · 1⤊ 0⤋
Integral x^4/8 = (1/8)Integral x^4 = (1/8)(1/5)x^5 + constant
2007-06-14 14:59:09 · answer #2 · answered by kellenraid 6 · 0⤊ 0⤋
use the integration rule that int(x^n) = x^n+1/(n+1) + C. so in your case int(x^4/8) = x^5/(8*5)+ C = x^5/40 +C
2007-06-14 15:00:11 · answer #3 · answered by Jared D 2 · 1⤊ 0⤋
(x^5)/40 + C, where C is any constant.
You can take the derivative of my answer in order to see why it works.
2007-06-14 15:00:00 · answer #4 · answered by math guy 6 · 1⤊ 0⤋
I think the word you're looking for is integration
2007-06-14 14:59:08 · answer #5 · answered by rosie recipe 7 · 0⤊ 1⤋