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Let f(x) = x + sin x . Suppose 'g' denot...

Let f(x) = x + sin x . Suppose 'g' denotes the inverse function of
'f' . The value of `g^' (pi/4 + 1/sqrt2)` has the value equal to

A

`sqrt2 - 1`

B

`(sqrt2 + 1)/sqrt2`

C

`2 - sqrt2`

D

`sqrt2 + 1`

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. int (sec x dx)/([sin(2x+alpha) + sin alpha]^(1/2)) is

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  2. If int (cos^4 x dx)/(sin^3 x (sin^5 x + cos^5 x)^(3/5)) is equal to -1...

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  3. Let f(x) = x + sin x . Suppose 'g' denotes the inverse function of 'f...

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  4. I = int 1/(cos^4 x) dx is equal to

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  5. int (x + 5)/((x-1)^2 (x-2)) dx =

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  6. int (3 + 2 cos x)/(2 + 3 cos x)^2 dx is equal to

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  7. int (x^2 - 1)/((x^2 +1) sqrt(x^4 + 1)) dx is equal to ?

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  8. I = int (x + x^(2/3) + x^(1/6))/(x (1+x^(1/3))) dx is equal

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  9. int (x^2 - 1)/((x^3)sqrt(2x^4- 2x^2 + 1)) dx is equal to

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  10. The value of the integral int e^(sin^2 x) (cos x + cos^3 x) sin x dx i...

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  11. int xabsx dx =

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  12. If f(x) = x^2, then /\^2 f(x) is

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  13. Integral of sqrt(1 + 2cot x (cot x + cosec x)) w.r.t.x, is

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  14. int (e^(2001x) + e^(1999x))/(e^x + e^-x) dx is

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  15. The primitive of the function f(x) =xabs(cosx), when x in (pi/2, pi) i...

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  16. If int tan^4 x dx = a tan^3 x + b tan x + phi(x) then

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  17. If int sinx/sin(x-alpha) dx = Ax + B log sin(x - alpha) + c

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  18. If int (4e^x + 6e^-x)/(9e^x - 4e^-x) dx = Ax + B loge(9e^(2x) - 4) + c...

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  19. If int x log(1 + x^2) dx = phi(x) log(1 + x^2) + psi(x) + c then

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  20. int dx/((x+1)(x-2)) = A log (x + 1) + B log (x - 2) + c where

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