A calculus problem by Aly Ahmed

$\displaystyle \int_0^{15} \displaystyle \int_0^{10} (x^2+y^2)dydx=\displaystyle \int_0^{15} (10x^2+\frac{1000}{3})dx=\dfrac{10\times 15^3}{3}+\dfrac{15\times 10^3}{3}=\boxed {16250}$ .

$\begin{aligned} \int_0^{15} \int_0^{10} \left(x^2 + y^2\right) dy \ dx & = \int_0^{15} \left[x^2y + \frac {y^3}3 \right]_0^{10} \ dx \\ & = \int_0^{15} \left(10 x^2 + \frac {1000}3 \right) \ dx \\ & = \frac {10x^3}3 + \frac {1000x}3 \ \bigg|_0^{15} \\ & = 11250 + 5000 \\ & = \boxed{16250} \end{aligned}$