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If I(n) = int(0)^(1)(dx)/((1+x^(2))^(n))...

If `I_(n) = int_(0)^(1)(dx)/((1+x^(2))^(n)) , n in N`, then which of the following statement hold good ?

A

`2n I_(n+1) = 2^( n) + (2n-1) I_(n)`

B

`I_(2) = pi/8+ 1/4`

C

`I_(2) = pi/8-1/4`

D

`I_(3) = pi/16-5/48`

Text Solution

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The correct Answer is:
A, B
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
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  2. The value of integral int(a)^(b)(|x|)/(x)dx, a lt b is :

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  3. If I(n) = int(0)^(1)(dx)/((1+x^(2))^(n)) , n in N, then which of the f...

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  4. The value of integral int0^pi xf(sinx)dx=

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  5. If I = int(0)^(2x)sin^(2)xdx, then

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  6. Given an even function f defined and integrable everywhere and periodi...

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  7. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

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  8. If a,b in R^(+) then find Lim(nrarroo) sum(k=1)^(n) ( n)/((k+an)(k+bn...

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  9. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

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

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

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

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

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

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

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

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

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

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

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

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