# Area under the ROC curve approximation

I wanted to compute the Area under the ROC curve for a logistic regression model in the context of binary classification. For that I computed, for a list of thresholds, say 0.1 0.2 ... 0.9, the TPR and FPR. I have thus

 (TPR_threshold1, ... TPR_thresholdN)
(FPR_threshold1, ... FPR_thresholdN)


Can I just do

TPR_threshold1*FPR_threshold1 + ... + TPR_thresholdN*FPR_thresholdN


in order to compute the area under the roc curve or do I need some more elaborate mathematical modeling?

Thanks a lot!