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

`If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx.` then

A

`(pi)/(4)-J`

B

2J

C

J

D

`(1)/(2).J`

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate : int0^(pi/2)(2logsinx-logsin2x)\ dx

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  17. If int0^(pi)xf(sinx)dx=Aint0^(pi/2)f(sinx)dx, then A is

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  18. The integral underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx vanishes...

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  19. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  20. The value int(-2)^(2) (plog ((1+x)/(1-x)) + q log ((1-x)/(1+x))^(-2) +...

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