Mathematics - Definite Integration Question with Solution | TestHub

On each interval where $\lfloor x\rfloor$ is constant, the integrand is the derivative of $e^{x\lfloor x\rfloor +x^2\lfloor x{\rfloor }^2+x^3\lfloor x{\rfloor }^3}$. Splitting at 2 gives $\left(e^{14}-e^3\right)+\left(e^{258}-e^{84}\right)$, hence $a=3.00$.