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int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi...

`int_(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx` is equal to

A

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

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  2. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

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  3. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

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  4. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx, where 'a' is positiv...

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  5. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

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  6. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

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  7. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

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  8. lim(n rarr infty) sum(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equa...

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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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  10. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

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  11. int(0)^(infty)f(x+(1)/(x)). (In x )/(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 g(x) is the inverse of f(x) and f(x) has domain x in [1,5], where...

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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)= int(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable functi...

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

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  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

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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+2}{x^3+4})dx, where {*} denotet th...

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