Question

Which of the definite integrals is bigger (top row = 2 and bottom row 1 for both) whether it is x^2 or x^3

Answer 1

\[\Large \int\limits_{1}^{2}x^2 dx\]\[\Large \int\limits\limits_{1}^{2}x^3 dx\]
Integral means finding the area under the curve. Which do you think has a bigger area in this graph?
http://www.wolframalpha.com/input/?i=y%3Dx%5E2+and+y%3Dx%5E3+from+x%3D1+to+x%3D2

Answer 2

without calculation

Answer 3

I need to know it without calculation

Answer 4

That is without calculation.

Answer 5

Or you can use the fact that \[\Large x^3 > x^2\]as long as x>1