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Let I(n) = int(0)^(1//2)(1)/(sqrt(1-x^(n...

Let `I_(n) = int_(0)^(1//2)(1)/(sqrt(1-x^(n))) dx` where `n gt 2`, then

A

`I_(n) lt pi/6`

B

`I_(n) gt pi/6`

C

`I_(n) lt 1/2`

D

`I_(n) gt 1/2`

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The correct Answer is:
A, D
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
  1. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

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  2. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

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  3. Let I(n) = int(0)^(1//2)(1)/(sqrt(1-x^(n))) dx where n gt 2, then

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  4. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

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  5. Let f(x) = int(0)^(x)|2t-3|dt, then f is

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  6. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

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  7. Let f(x) be a function satisfying f(x) f(x+2) = 10 AA x in R, then

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  8. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

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  9. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

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  10. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

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  11. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

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  12. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

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  13. Let f(x) is a quadratic expression with positive integral coefficient...

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

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  15. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

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  16. lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...

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  17. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

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  18. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

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  19. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,a n dt h ex-a xi sd...

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  20. Let f(x) be a non-negative, continuous and even function such that are...

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