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If f(x)=int(-1)^(x)|t|dt, then for any x...

If `f(x)=int_(-1)^(x)|t|dt`, then for any `x ge0,f(x)` is equal to

A

`1/2(1-x^(2))`

B

`1-x^(2)`

C

`1/2(1+x^(2))`

D

`1+x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
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  2. int- 5^5|x+2|dx

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  4. int(0)^(1)|3x-1|dx=

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  5. int-2^2 |1-x^2|dx= (A) 4 (B) 2 (C) -2 (D) 0

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  6. The value of int(0)^(1)x|x-1/2|dx is

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  7. int(0)^(100pi)|cosx|dx=…………………………..

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  8. int(0)^(pi//2) abs(sinx-cosx) dx=

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  9. The integral int(0)^(pi)sqrt(1+4"sin"^2(x)/(2)-4"sin"(x)/(2)) dx is e...

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  10. If I=int(1/ e)^e|logx|(dx)/(x^2) ,then I equals (A) 2 (B) 2...

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  11. int(0) ^(3) [x] dx= where [x] is greatest integer function

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  12. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

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  13. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  14. The value of int0^9[sqrt(x)+2]dx, where [.] is the greatest integer fu...

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  15. If for all real numbers y ,[y] is the greatest integer less than or eq...

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

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

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

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  19. int- 2^2[x]dx

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

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