Home
Class 12
MATHS
int0^pi[cotx]dx , where [.] denotes the ...

`int_0^pi[cotx]dx` , where [.] denotes the greatest integer function, is equal to (1) `pi//2` (2) 1 (3) `1` (4) `pi//2`

Text Solution

Verified by Experts

`I = int_0^pi [ cot x] dx`
`= int_0^pi [ cot(pi- x)] dx`
`= int_0^pi [cot(pi-x)] dx`
`= int _0^ pi [ - cot x] dx`
`(i) + (ii)`
`2 I= int_0^pi [ cot x] + int_0^pi [-cot x] dx`
`[x] + [-x] = -1 x !in z`
`= 0 x !in z`
...
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|22 Videos

  • VECTOR ALGEBRA

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|19 Videos

Similar Questions

Explore conceptually related problems

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

int_(0)^(2pi)[|sin x|+|cos x|]dx , where [.] denotes the greatest integer function, is equal to :

int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

int_0^(sqrt(pi/2))[[x^2]+cosx]dx (where [.] denotes greatest integer function)

Evaluate: int_(0)^(2 pi)[sin x]dx, where [.] denotes the greatest integer function.

int_(1)^(10pi)([sec^(-1)x]+[cot^(-1)x])dx , where [.] denotes the greatest integer function, is equal to:

The value of int_(-1)^(3){|x-2|+[x]} dx , where [.] denotes the greatest integer function, is equal to