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T h ev a l u eofint(-2)^1[x[1+cos((pix)/...

`T h ev a l u eofint_(-2)^1[x[1+cos((pix)/2)]+1]dx ,` where [.] denotes the greatest integer function, is 1 (b) `1//2` (c) 2 (d) none of these

A

1

B

`1//2`

C

2

D

None of these

Text Solution

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The correct Answer is:
C
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If f(x)={e^(cosxsinx ,for|x|lt=2)2,ot h e r w i s e ,t h e nint(-2)^3f...

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  2. The value of int0^(pi/3) [sqrt3 tanx]dx( where [.] denotes the greates...

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  3. T h ev a l u eofint(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes ...

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  4. int (0)^(2) x ^(3) [1+ cos ""(pix)/(2)] dx is (where [**] denotes the ...

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  5. Let f(x)=minimum {|x|,1-|x|,1/4} for xepsilonR then the value of int-1...

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

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  7. If f(n)=(int0^n[x]dx)/(int0^n{x}dx)(where,[*] and {*} denotes greatest...

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  8. int (0) ^(2npi) (|sin x | - [|(sin x )/(2) | ]) dx is equal to (where ...

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  9. The value of int (0) ^([x]){x} dx is

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  10. If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) an...

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  11. If f(a+b - x) = f(x) , then int(a)^(b) x f(x) dx is equal to

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  12. If int(0)^(pi) x f (sin x) dx = A int (0)^(pi//2) f(sin x) dx , then A...

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  13. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

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  14. The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x)dx where agt 0, is

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  15. overset(pi//2)underset(-pi//2)int (|x|)/(8 cos^(2)2x+1)dxhas the value

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  16. int(0)^(pi//2)(1)/(1+tan^(3)x)dx=

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  17. int (-1) ^(1) (x ^(4))/( 1 + e ^(x ^(7)))dx is

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  18. int (-1) ^(1) (sin x + x ^(2))/( 3 - |x|) dx

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  19. The value of overset(pi//4)underset(-pi//4)int(e^(x)sec^(2)x)/(e^(2x)-...

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  20. int ( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ cos ^(2) x )

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