Home
Class 12
MATHS
The value of int(1)^(a)[x] f' (x) dx, a ...

The value of `int_(1)^(a)[x] f' (x) dx, a gt 1`, where `[x]` denotes the greatest integer not exceeding x is

A

`af(a)-{f(1)+f(2)+....+ f([a])}`

B

`[a]f(a)-{f(1)+f(2)+....+f([a])}`

C

`[a]f([a])-{f(1)+f(2)+....+f(a)}`

D

`af([a])-{f(1)+f(2)+....+f(a)}`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|151 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Examples|8 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - I|67 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(pi//3)[sqrt(3)tanx]dx (where [.] denotes the greatest integer function)

int_(0)^(pi) [cot x] dx , where [*] denotes the greatest integer function, is equal to

Evaluate int_(0)^(100)e^(x-[x])dx where [ ] denotes the greatest integer function.

If f: R rarr R and g:R rarr R are defined by f(x)=x - [x] and g(x)=[x] for x in R , where [x] is the greatest integer not exceeding x , then for every x in R, f(g(x))=

If f:RR rarr RR is defined by f(x)=[(x)/(2)] for x in RR , where [y] denotes the greatest integer not exceeding, y then {f(x):|x| lt 71}=

The range of sin^(-1)[x^(2)+1/2] + cos^(-1)[x^(2)- 1/2] , where [.] denotes the greatest integer function, is

If f: R rarr R is defined by f(x)= [x/5] for x in R , where [y] denotes the greatest integer not exceding y, then {f(x):|x| lt 71}=