Let I=int0^n[x]dx,n > 0, where [ ] is G....

Let `I=int_0^n[x]dx,n > 0,` where [ ] is G.I.F.,

A

`n`

B

`(n(n+1))/2`

C

`(n(n-1))/2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

C

Topper's Solved these Questions

DEFINITE INTEGRALS
TARGET PUBLICATION|Exercise COMPETITIVE THINKING|148 Videos
CONTINUITY
TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
DIFFERENTIAL EQUATIONS
TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

The value of int_0^5([x]+|x-2|)dx , where [.] represents G.I.F. is

The value of int_(0)^(2)[x]*x^(2)dx is (where [*]rarr G.I.F)

The value of int_(0)^(2)[x]*x^(2)dx is (where [*]rarr G.I.F

Let I_(n) = int_(0)^(1) (logx)^(n)dx , where n is a non-negative integer. Then I_(2001) - 2011 I_(2010) is equal to -

Let I_(n)=int_(0)^(pi//2)x^(n)cosxdx, where in is a non-negative integer Then sum_(n=2)^(oo)((I_(n))/(n!)+(I_(n-2))/((n-2)!)) equals-

Let f(x) is a continuous function symmetric about the lines x=1a n dx=2. If int_0^(2)f(x)dx=3 and int_0^(50)f(x)=I , then [sqrt(I)] is equal to (where [.] is G.I.F.) (a)5 (b) 8 (c) 7 (d) 6

The value of definite integral int_0^10 ([x] + |x-2|)dx , where [.] represents G.I.F. is

LetI_(1)=int_(0)^(n)[x]dx and I_(2)=int_(0)^(n){x}dx where [x] and {x} are integral and fractionalparts of x and n in N-{1}. Then (I_(1))/(I_(2)) is equal to

TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST

If f(x)+f(3-x)=0,then int(0)^(3)1/(1+2^(f(x)))dx=
Text Solution
|
int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=
Text Solution
|
Let I=int0^n[x]dx,n > 0, where [ ] is G.I.F.,
Text Solution
|
If In = int0^(pi/2) (sin^2 nx)/(sin^2 x) dx, then
Text Solution
|
The value of the integral intalpha^beta 1/(sqrt((x-alpha)(beta-x)))dx
Text Solution
|
Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...
Text Solution
|
If m and n are positive integers and f(m,n)=int(0)^(1)x^(n-1)(logx)^(m...
Text Solution
|
The least value of the function phi(x)=int((7pi)/6)^(x)(4sint+3cost)dt...
Text Solution
|
Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx
Text Solution
|
The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...
Text Solution
|
If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...
Text Solution
|
lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...
Text Solution
|
lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)
Text Solution
|
Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...
Text Solution
|
int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=
Text Solution
|
I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...
Text Solution
|
overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...
Text Solution
|
The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...
Text Solution
|
int(0)^(sqrt("log"(pi)/2))cos(e^(x^(2)))2xe^(x^(2))dx=
Text Solution
|
If f(x)=int(0)^(x)sin^(6)tdt, then f(x+pi)=
Text Solution
|