The value of _ 1 ^ a [ x ] f ´ (x) dx, a > 1, where [x] denotes the greatest integer not…
Mathematics · JEE Main · NTA Exams — Integral Calculus
The value of \(\int_{1}^{\mathrm{a}}[\mathrm{x}]\) f ´ (x) dx, a > 1, where [x] denotes the greatest integer not exceeding x, is
- a f ( a) –{ f (1) + f (2) + ... + f ([a])}
- [a] f (a ) – { f (1) + f (2) + ... + f ([a])}
- [a] f ([a]) – { f (1) + f (2) + ... + f (a )}
- af ([a]) – { f (1) + f (2) + ... + f (a )}
Answer
(B) [a] f (a ) – f (1) + f (2) + ... + f ([a])
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