I was trying the integration of Amazon API gateway with Lambda function. I was successfully able to achieve though but when I tried with curl it fails.
Lambda method
In my case the problem was that I did not Deploy the API, so it was not updated for external use. See Amazon API Gateway : response body is not transformed when the API is called via Postman?
Please make sure your content-type what you defined in integration request template.
You can try this curl command.
curl -X POST https://aaaaaaa.execute-api.us-west-2.amazonaws.com/beta/apitest/xml -H "Content-Type: application/json" --data-binary "Articletext"