AP Calculus AB and BC glossary

Limits of integration

The limits of integration are the two numbers attached to a definite integral, marking where the accumulation starts and stops. When you substitute, either convert them to the new variable or convert the antiderivative back before evaluating.

abf(x)dx\int_{a}^{b} f(x)\,dx

Swapping the limits negates the integral, and equal limits make it zero. Both are properties worth knowing, because they turn awkward setups into short ones.

The mistake

Substituting u but leaving the original x limits in place. Either change the bounds to u values or convert back to x first; mixing the two is the classic substitution error.

Appears in: Unit 6: Integration and Accumulation