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Let a gt 0 and f(x) is monotonic increa...

Let `a gt 0 and f(x) ` is monotonic increase such that `f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx ` is equal to
(a)`a+b``" "`(b)`ab+b`
(c)`ab+a``" "`(d)`ab`

A

(a)`a+b`

B

(b)`ab+b`

C

(c)`ab+a`

D

(d)ab

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
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  9. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

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  11. The value of int (0)^(infty)e^-(a^(2)x) dx is equal to

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  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

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  13. If 2f (x) +f (-x)=(1)/(x) sin (x-(1)/(x)), then the value of int(1//e...

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  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

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  15. If f(x) is differentiable function and (f(x).g(x)) is differentiable a...

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  16. The number of integral solutions of the equation 4int (0)^( infty)(log...

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  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

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  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

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  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+3}{x^2+4})dx, where { } denote the...

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