Archimedes's Method

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Q. Which of the following gives the area under the curve $y=x^2$, between x = 0 and x = b?

1. $\sum \frac{b^2}{n^2}{k}^3$, where k varies from 1 to n and n tends to infinity
2. $\sum \frac{b^3}{n^3}{k}^2$, where k varies from 1 to n and n tends to infinity
3. $\sum \frac{b^2}{n^2}{k}^2$, where k varies from 1 to n and n tends to infinity
4. $\sum \frac{b^3}{n^3}{k}^3$, where k varies from 1 to n and n tends to infinity

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Q. In Archimedes's method for finding the area of a curve(function), we divide the area into intervals of width ‘1 unit’ and construct rectangles of width ‘1 unit’ and height as the value of the function on the rightmost point of the interval.

1. True
2. False

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