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inta^b(logx)/x\ dx=1/2log(a b)\ log(b/a)...

`int_a^b(logx)/x\ dx=1/2log(a b)\ log(b/a)`

A

`log((log b)/(log a))`

B

`log (ab).log((b)/(a))`

C

`(1)/(2).log(ab).log((b)/(a))`

D

`(1)/(2).log(ab).log((a)/(b))`

Text Solution

Verified by Experts

The correct Answer is:
C
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MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
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  2. int(-pi)^(pi)sin^(2)x.cos^(2)x dx=

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  3. inta^b(logx)/x\ dx=1/2log(a b)\ log(b/a)

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  4. int(0)^(pi//2)sin x.sin 2x dx=

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

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  6. int(0)^(a)(x)/(sqrt(a^(2)+x^(2)))dx

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  7. int(0)^(pi//2)(cos x)/(1+sin x + cos x)dx=

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  8. int(0)^(pi//2)(sin x.cos x)/(1+sin^(4)x)dx=

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  9. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

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  10. If : x(x^(4)+1).f(x)=1, then : int(1)^(2)f(x)dx=

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  11. int(0) ^(pi//2) ((sin x +cos x )^(2))/sqrt(1+ sin 2x)dx =

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  12. If : int(0)^(2a)f(x)dx=2.int(0)^(a)f(x)dx, then :

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  13. If I = int(0)^(pi//4) sin^(2) x" "dx and J = int(0)^(pi//4)cos^(2)x" "...

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  14. int(-1)^(1)(sqrt(1+x+x^(2))-sqrt(1-x+x^(2)))dx=

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  15. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

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  16. Suppose f is such that f(-x)=-f(x) for every real x and int0^1 f(x) dx...

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  17. If f(x) = tan x - tan^(3) x + tan^(5) x - ….oo with 0 lt x lt pi/4 ...

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  18. int(1/n)^((an-1)/n) sqrt(x)/(sqrt(a-x)+sqrt(x))dx= (A) a/2 (B) (na+2)/...

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  19. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

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  20. lim(n to oo)[(n)/(1+n^(2))+(n)/(4+n^(2))+(n)/(9+n^(2))+…+(1)/(2n^2)]=

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