Мысал 5. және сызықтарымен шенелген фигураның ауданын есептеу керек.
Шешуі Берілген сызықтардың қиылысу нүктелерінің абсциссаларын теңдеуінен табамыз. Теңдеудің шешімі . х-тің осы мәндері интегралдау шекаралары болады. Сондықтан, (2) формуласы бойынша
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