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

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

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`(pi)/(6)`

D

`(pi)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
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MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
  1. int(0)^(a)(x)/(sqrt(a^(2)+x^(2)))dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate lim(n->oo) [1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3) +......

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  17. lim(n->oo)1/nsum(r=1)^(2n)r/(sqrt(n^2+r^2)) equals

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  18. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  19. The solution for x of the equation int(sqrt(2))^x(dt)/(tsqrt(t^2-1))=p...

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  20. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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