The value of $\int_{1}^{3}[x-1] d x$, where $[x]$ denotes the greatest integer function in $x$, is e

Question

The value of $\int_{1}^{3}[x-1] d x$, where $[x]$ denotes the greatest integer function in $x$, is equal to\

Professor PC Thomas Classes · Answer

(d) : Let $I=\int_{1}^{3}[x-1] d x=\int_{1}^{2}[x-1] d x+\int_{2}^{3}[x-1] d x$\ $=\int_{1}^{2} 0 \cdot d x+\int_{2}^{3} 1 \cdot d x=0+\left.xight|_{2} ^{3}=(3-2)=1$\