If $$[x]$$ is the greatest integer function not greater than $$x$$, then $$\int_\limits0^8[x] d x$$ is equal to

$$\int_0^{\pi / 2} \sqrt{\sin \theta} \cos ^3 \theta d \theta$$ is equal to

$$\int_0^1 \frac{x e^x}{(2+x)^3} d x$$ is equal to

Evaluate $$\int_\limits2^3 x^2 d x$$ as the limit of a sum