TheAWS_PROXY integration with Amazon API Gatewayallows the API to invoke a Lambda function synchronously, making it a suitable solution for the custom authorization mechanism and text translation use case.

Synchronous Invocation: The API Gateway REST API with AWS_PROXY integration enables synchronous processing of HTTP requests and responses, which is required for document translation.

Custom Authorization: API Gateway supports custom authorizers for fine-grained access control.

Lambda Function Execution: Although Lambda's execution time limit is 15 minutes, this is sufficient for the 6-minute document translation requirement.

Why Other Options Are Not Ideal:

Option B:

Introducing a Lambda function URL to invoke another Lambda function unnecessarily complicates the architecture.Not efficient.

Option C:

Asynchronous invocation cannot guarantee real-time response delivery for document translation tasks.Not suitable.

Option D:

Hosting the API on an EC2 instance increases operational overhead. HTTP PROXY integration does not add significant benefits here.Not cost-effective or efficient.

AWS References:

API Gateway Lambda Proxy Integration:AWS Documentation - Proxy Integration

Custom Authorization in API Gateway:AWS Documentation - Custom Authorization