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Let f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2));...

Let `f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2)); x in R,` then

A

strictly increases `AA x in R`

B

strictly increases only in `(0,oo)`

C

strictly decreases `AA x in R`

D

strictly decreases in `(o,oo)` and strictly increases I `(-oo, 0)`

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The correct Answer is:
A
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VIKAS GUPTA (BLACK BOOK)-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2)); x in R, then

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  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

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  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

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  4. Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x) be its inverse. ...

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  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

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  6. If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(s...

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

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  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

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  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

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  11. Find the value of |a| for which the area of triangle included between ...

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  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  13. If maximum value of int (0)^(1) (f (x ))^(2) dx under the condition -1...

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  14. Let a differentiable function f (x) satisfies f (x). F '(-x) . F'(x) a...

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  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

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  16. Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...

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  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

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  21. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

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