alleryStart learning →For a definite integral with limits swapped, which identity holds?
- $\int_a^b f\,dx = \int_b^a f\,dx$
- $\int_a^b f\,dx = -\int_b^a f\,dx$
- $\int_a^b f\,dx = \int_b^a f\,dx + c$
- $\int_a^b f\,dx = 1/\int_b^a f\,dx$
Show answer and solution
Correct answer: B. $\int_a^b f\,dx = -\int_b^a f\,dx$
**Property II:** swapping limits flips the sign.
$\int_a^b f\,dx = g(b)-g(a) = -[g(a)-g(b)] = -\int_b^a f\,dx$.