Re: Another question regarding integration.....
Originally posted by Saintly Devil
Which one is the answer to the indefinite integral of d(x^3)/dx (i.e. the integration of the differentiation of x cubed):
1) x^3 +C
2) x^3
I thought it was 2), since you already know the initial 'y' value, and so by integrating it's derivative, there is really no unknown.
But my teacher said it was x^3 + C. Can anyone explain why this is/isn't the case?
Thanks
tooheyz, that was pretty confusing
but he meant the result when x^3 is differentiated, integrated
or the differential of x^3, integrated.
either way, differentiate first, and integrate
(what's the point! differentiating and reversing the process via integration... -1 to the power, +1 to the power ... amazing
)
but anyway, the answer is 1)
because indefinite integrals have no 'restrictions' per se (terminals, end points) so you need the constant +C, +k as tooheyz stated.
d/dx x^3 = 3x^2 (simple enough)
integrate 3x^2 and you get 3x^3 on 3 (add 1 to the power, divide by the new power), and simplifying
3x^3
------- +C
3
= x^3 + C is your answer #
answer 2) would apply if you were given end points e.g. x = 1, x = 5 or whatever and you'd sub in the values, from a to b and
subtract as you would normally
