Performing integration using hardware instead of software
Generally analog circuits like this aren't used in computers chips except for I/O and power delivery. The reason for this is that in the space that you can put an IC capacitor, you could have thousands if not millions of transistors. Capacitors eat up IC real estate. This is why the world has gone digital in general. Lots of transistors can be squeezed onto ICs. 

As mentioned in my comment, there's other limitations of an analog integrator such as input offset error amplification and the bandwidth is small. 

If there was a large enough application for needing integration in HPC, they would add digital hardware integrators into the cpu's or accelerators.