0
$\begingroup$

As you know we can solve definite integrals using the definition over limit (without using antiderivatives at all). So I what I ask is how to solve an indefinite integral like that? For example $$\int x^2 \, dx$$ , we all know the result is x^3/3 + c. But we got this by using differentation and Fundamental Theorem of Calculus. How can we calculate this without using them?

$\endgroup$
1
  • $\begingroup$ Indefinite integrals are by definition anti-derivatives. There is no direct limit definition for them. $\endgroup$ – Paramanand Singh Jan 6 '19 at 16:43
1
$\begingroup$

Divide the interval into n parts and use $\sum_{k=1}^n k^2 =n(n+1)(2n+1)/6 =n^3/3+$ smaller terms.

Take the limit.

This is how these integrals were originally found.

$\endgroup$
1
  • $\begingroup$ Can you write the exact limit expression? It seems easy this way but I need it to understand for real. $\endgroup$ – madscientist Jan 7 '19 at 18:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.