Question

Evaluate:
\[ \huge \int_0^1 \int_\sqrt{y}^1 \sqrt{x^3+1} \, dx \, dy \]

Answer 1

what's in the lower limit?

Answer 2

\[\huge =\int\limits_{0}^{1} \int\limits_{0}^{x^2} \sqrt{1+x^3} dy dx\]

Answer 3

nice ... i always get confused on these stuff!!!

Answer 4

Thanks. The y integral gives \[\int\limits_{0}^{1}\int\limits_{0}^{x^2} \sqrt{1+x^3} dx dy = \int\limits_{0}^{1} x^2\sqrt{1+x^3} dx\]

then just switch variables to x^3.

Answer 5

yep ... pretty confusing ... if you try to do it directly.
in the end geometry saves he day!!

Answer 6

*the