True or false question about areas under curves ?

The area under the graph of a positive continuous function can be computed by finding the limit of sums of areas of rectangles. True or False.





I think the statement is true but the positive continuous function confuses me a little. Thanks for any help.





True or false question about areas under curves ?
True. This is the integration.


The positive continuous function just means it is always above the x axis. This allows the statement to be true. If it was not positive, the area could not be computed by sums of areas of rectangles, because there would be a 'negative' value when the function would go below the x axisTrue or false question about areas under curves ?
This is true and is the definition of a definite integral as a sum of rectangles of infinitely small width.
Later you should learn that you can weaken the statement to positive, bounded, piecewise continuous