GUIDE深度 · Deep dive
Definite Integrals and Limits
For a definite integral, find an antiderivative, then evaluate upper minus lower. For limits, simplify/factor and cancel before substituting; do not substitute when the denominator is 0.
Definite integral
∫ x^2 dx = x^3/3 + C.
∫_0^2 x^2 dx = 8/3.
Limits
(x^2-a^2)/(x-a) = x+a for x != a.
Cancel, substitute x=a, get 2a.
FAQ
Add C to definite integrals?
No; C cancels when subtracting bounds.
Can I substitute directly?
Yes if the denominator is not 0; simplify 0/0 first.