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Let a function f:R to R be defined as f ...

Let a function `f:R to R` be defined as `f (x) =x+ sin x.` The value of `int _(0) ^(2pi)f ^(-1)(x) dx` will be:

A

`2pi^(2)`

B

`2pi^(2)-2`

C

`2x ^(2) +2`

D

`pi^(2)`

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The correct Answer is:
A
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VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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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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  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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

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  16. int( x^3)/(x^2-2)dx

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  17. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

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

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  19. Find the vlaur of lim (n to oo) (1)/(sqrtn)(1+ (1)/(sqrt2) +(1)/(sqrt3...

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  20. The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...

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