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int(0)^(pi)[cos x] dx, [ ] denotes the g...

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

A

`pi/2`

B

`0`

C

`-1`

D

`- pi/2`

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The correct Answer is:
D
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MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-Questions from Previous Years. AIEEE/ JEE Main Papers
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  2. If for n ge 1, P(n) = int(1)^( e) (log x)^(n) dx, then P(10) - 90P(8) ...

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  3. int(0)^(pi)[cos x] dx, [ ] denotes the greatest integer function , is ...

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  4. If for a continuous function f(x), int(-pi)^(t) (f(x)+ x) dx= pi^(2) -...

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  5. Let function F be defined as f(x)= int1^x e^t/t dt x > 0 then the v...

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  6. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

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  7. Let f: RR rarr RR be a function such that f(2 - x) =f(2 + x) and f(4-x...

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  8. Let f : (-1,1) to R be continous function , if int (0)^(sinx) f(t)...

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  9. If f(x)=underset(1)overset(x)int (log t)/(1+t) dt"then" f(x)+f((1)/(x)...

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  10. If 2int0^1 tan^(-1)x dx= int0^1 cot^(-1)(1-x+x^2) dx then int0^1 tan^(...

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  11. underset (n rarr infty )(lim) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is e...

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  12. int4^10([x^2])/([x^2-28 x+196]+[x^2])dx is (A) 3 (B) 5 (C) 7 (D) 9

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  13. The integral int(pi/12)^(pi/4)(8cos2x)/((tanx+cotx)^3)dx equals

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  14. If int(1)^(2) (dx)/( (x^(2) -2x + 4)^(3/2))=(k)/( k+5) then k is equal...

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  15. int(pi//4)^(3pi//4)(dx)/(1+cos x)=

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  16. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

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  17. If i is the greatest of the definite integrals I1=int0^1 e^-x cos ^2 ...

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  18. The value of the integral int(-pi//2)^(pi//2) sin^(4) x (1+ log ((2+ s...

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  19. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx is

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  20. The value of int(0)^(pi)|cos x|^(3)dx is :

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