This Letter reports on a cavity haloscope search for dark matter axions in the Galactic halo in the mass range 2.81-3.31 μeV. This search utilizes the combination of a low-noise Josephson parametric amplifier and a large-cavity haloscope to achieve unprecedented sensitivity across this mass range. This search excludes the full range of axion-photon coupling values predicted in benchmark models of the invisible axion that solve the strong CP problem of quantum chromodynamics.