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The value of int(1)^(a)[x]f'(x)dx, where...

The value of `int_(1)^(a)[x]f'(x)dx,` where `agt1`, and `[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

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The correct Answer is:
B
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. If for all real numbers y ,[y] is the greatest integer less than or eq...

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  2. int(0)^((pi)/2)(x-[cosx])dx= (where [t]= greatest integer less or eq...

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  3. The value of int(1)^(a)[x]f'(x)dx, where agt1, and [x] denotes the gre...

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  4. If [x] denotes the greatest integer less than or equal to x then the v...

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  5. int- 2^2[x]dx

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  6. If [x] dentoes the greatest integer less than or equal to x, then the ...

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  7. int(0)^(11)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=

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  8. int0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx

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  9. int(0)^((pi)/2)(sin^(1000)x dx)/(sin^(1000)x+cos^(1000)x) is equal to

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  10. int(0)^((pi)/2)(tan^(7)x)/(cot^(7)x+tan^(7)x)dx is equal to

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  11. The value of the integral int(0)^(pi//2)(sqrt(cotx))/(sqrt(cotx)+sqrt(...

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  12. int(0) ^( pi//2) (root(n)(secx))/(root(n) (secx )+ root (n) ("cosec "x...

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  13. Evaluate the following : int(0)^(pi//2)(1)/(1+sqrt(tanx))dx

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  14. int(0)^((pi)/2)(dx)/(1+(tanx)^(sqrt(2018)))=

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  15. The value of int (0)^(pi//2) (2^(sinx))/(2^(sinx)+2^(cosx))dx is

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  16. int(0)^((pi)/2)(2008^(sinx))/(2008^(sinx)+2008^(cosx))dx=

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  17. int(0)^((pi)/2)(cos^(3)x)/(sinx+cosx)dx

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  18. int(0)^(pi//2) log (cotx ) dx=

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  19. If int(0)^((pi)/2)log(cosx)dx=-(pi)/2log2, then int(0)^((pi)/2)log(cos...

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  20. int(0)^(pi//2) sin 2x log (tan x) dx is equal to

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