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Let f be a non constant continuous funct...

Let f be a non constant continuous function for all `xge0`. Let f satisfy the relation `f(x)f(a-x)=1` for some `a in R^(+)`. Then `I=int_(0)^(a)(dx)/(1+f(x))` is equal to

A

a

B

`a/4`

C

`a/2`

D

`f(a)`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. int(0)^(pi//2) sin 2x log (tan x) dx is equal to

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  2. int(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

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  3. Let f be a non constant continuous function for all xge0. Let f satisf...

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  4. int(0)^(pi)(xdx)/(1+sinx) is equal to

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  5. int(0)^(pi)(x dx)/(4 cos^(2)x+9sin^(2)x)=

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  6. int0^pi(ntanx)/(secx+cosx)dx

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  7. int0^(pi/2) (xsinxcosx)/(cos^4x+sin^4x) dx=

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  8. int0^1log(1+x)/(1+x^2)dx

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  9. The value of int(8 log(1+x))/(1+x^(2)) dx is

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  10. int(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, ...

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  11. int2^8 sqrt(10-x)/(sqrtx+sqrt(10-x))dx

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  12. int(2016)^(2017)(sqrt(x))/(sqrt(x)+sqrt(4033-x))dx is equal to

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  13. int(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

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

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  15. The value of int(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

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  16. The value of overset(sqrt("In"3))underset(sqrt("In"2))int(xsinx^(2))/(...

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  17. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

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  18. The value of the definite integral 1/pi int(pi/2)^((5pi)/2) e^(tan^(-...

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  19. If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e+pi), then inte^pi xf(x)dx is ...

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  20. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

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