∫20([x]2−[x2])dx is equal to
−4+√3+√2
∫20([x]2−[x2])dx=∫10([x]2−[x2])dx+∫21([x]2−[x2])dx=∫10(0−0)dx+∫211.dx−∫21[x2]dx
[ ∵ If x lies between 0 and 1, then x2 also lies between 0 and 1]
=0+1−[∫√21[x2]dx+∫√3√2[x2]dx+∫2√3[x2]dx]=1−[∫√211.dx+∫√3√22.dx+∫2√33.dx]=1−(√2−1)−2(√3−√2)−3(2−√3)=−4+√3+√2