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One problem with using rectangles to approximate an area under a curve is it will overestimate or underestimate the area, depending on which endpoint is used. The trapezoidal method gives a closer approximation.
That depends on how precise you want the approximation.
That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.
The best approximation is, of course, the exact value. A reasonable approximation is 106.
There is no reasonable radical approximation for radical 11.