Question Detail

Let's analyze each option:A: $\int_a^a f(x)dx = 0$. This is a fundamental property of definite integrals, stating that the integral over an interval of zero length is zero. This statement is correct.B: $\int_a^b f(x)dx = \int_b^a f(x)dx$. The correct property for reversing the limits of integration is $\int_a^b f(x)dx = -\int_b^a f(x)dx$. Therefore, the given statement is incorrect.C: $|\int_a^b f(x)dx| \leq \int_a^b |f(x)|dx$ if $a < b$. This is the Triangle Inequality for Integrals, which is a fundamental property. This statement is correct.D: $\int_a^b f(x)dx \leq \int_a^b g(x)dx$ if $f(x) \leq g(x)$ in $[a,b]$. This is the Comparison Property of Integrals, which is also a fundamental property. This statement is correct.Thus, option B is the incorrect equation.