If you are using the ArcGIS Runtime API (this is not ArcObjects), then take a look at the sample application which comes with the API. Go to the Network Analyst -> Service Area (online) sample.
The class you are interested in is called ServiceAreaTask.
If this question is an ArcObjects question, then this isn't a good place to put your question. This forum is for the ArcGIS Runtime SDK for Java. This product is not ArcObjects based.