Calculus

Confusing Definite and Indefinite Integrals

Students treat a definite integral and an indefinite integral as the same kind of answer.

Quick check

Why students make it

Both types of integrals use the integral symbol, so students focus on antidifferentiating and ignore whether bounds are present. They forget that bounds change the task from finding a family of functions to finding one number.

The rule done right

An indefinite integral has no bounds and gives a family of antiderivatives, so it needs +C+ C. A definite integral has bounds and gives a number, computed by ∫abf(x) dx=F(b)−F(a)\int_a^b f(x)\,dx = F(b) - F(a).

Related resources

integralsantiderivativesdefinite-integrals