Eduprobe
Question:
∫π0[cotx]dx, where [.] denotes the greatest integer function, is equal to
1
π/2
∞
-π/2
Solution:
LetI=∫π0[cotx]dx ... (i)Then, alsoI=∫π0[cot(π−x)]dx=∫π0[−cotx]dx... (ii)From (i) (ii) eqs, we get2I=∫π0[cotx]+[−cotx]dx
1
π/2
∞
-π/2
LetI=∫π0[cotx]dx ... (i)Then, alsoI=∫π0[cot(π−x)]dx=∫π0[−cotx]dx... (ii)From (i) (ii) eqs, we get2I=∫π0[cotx]+[−cotx]dx