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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

Verified by Experts

The correct Answer is:
C

From graph `int_(-2)^(1)[x[1+"cos"(pix)/2]+1]dx`
`=int_(-2)^(-1) [x[1+(-1)]+1]dx+int_(-1)^(1)[x[10]+1]dx`
`=(x)_(-2)^(-1)+int_(-1)^(1)[x+1]dx`
`=(-1-(-2))+int_(-1)^(0)0dx+int_(0)^(1)1dx=2`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  2. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

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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. Evaluate: int0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integ...

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  5. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  6. G i v e nint0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integr...

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  7. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

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  8. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

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  9. about to only mathematics

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  10. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

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  11. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I2=int(f...

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  12. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

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  13. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is sqrt(...

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  14. f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)(nvecoo)[int0^a(f(x)dx)/...

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  15. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,t h e nlambdai s...

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  16. The value of the definite integral int0^1(1+e^-x^2)dx (b) 2 1+e^...

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  17. T h ev a l u eoft h ein t egr a lint(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(...

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  18. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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  19. IfI1=int0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I2=int0^(pi/2)(sin^2x)/(1+sin^2...

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  20. Evaluate int(0)^(pi/2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx

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