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

Question

agent0smith · Answer

$$\Large \int\limits_{1}^{2}x^2 dx$$$$\Large \int\limits\limits_{1}^{2}x^3 dx$$ 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

anonymous · Answer

without calculation

anonymous · Answer

I need to know it without calculation

agent0smith · Answer

That is without calculation.

agent0smith · Answer

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