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Let I(n) = int(0)^(1)x^(n)(tan^(1)x)dx, ...

Let `I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N`, then

A

`(n+1)I_(n)+(n-1)I_(n-2)= (pi)/(4)+(1)/(n) AA n ge 3`

B

`(n+1)I_(n)+(n-1)I_(n-2)= (pi)/(2)-(1)/(n) AA n ge 3`

C

`(n+1)I_(n)-(n-1)I_(n-2)= (pi)/(2)+(1)/(n) AA n ge 3`

D

`(n+1)I_(n)-(n-1)I_(n-2)= (pi)/(2)-(1)/(n) AA n ge 3`

Text Solution

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The correct Answer is:
B
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - 1
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  2. If f(x) = int(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt, f(x+pi) is equal to :

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  4. Let f(x) is differentiable function satisfying 2int(1)^(2)f(tx) dt ...

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  5. Let I(n) = int(0)^(1)x^(n)(tan^(1)x)dx, n in N, then

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  6. If u(n) = int(0)^(pi//2) x^(n)sinxdx, then the value of u(10) + 90 u(...

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  7. The value of int(1//e)^(tanx)(t)/(1+t^(2))dt+int(1//e)^(cotx)(1)/(t(1+...

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  8. Let A(1) = int(0)^(x)(int(0)^(u)f(t)dt) dt and A(2) = int(0)^(x)f(u).(...

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  9. lim(nrarroo) (sin'(pi)/(2n).sin'(2pi)/(2n).sin'(3pi)/(2n)"......."sin'...

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  10. Area bounded by the region consisting of points (x,y) satisfying y le ...

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  11. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

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  12. The area bounded by the curve x = a cos^3t,, y = a sin^3t, is :

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  13. The area bounded by the curve f(x)=x+sinx and its inverse function bet...

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  14. P(2,2), Q(-2,2) R(-2,-2) & S(2,-2) are vertices of a square. A para...

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  15. The ratio in which the curve y = x^(2) divides the region bounded by ...

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  16. If f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi)a n df(x)...

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  17. The area bounded by the curves y = x e^(x), = x e^(-x) and the line ...

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  18. Obtain the area enclosed by region bounded by the curves y = x ln x an...

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  19. The area of the region on place bounded by max (|x|,|y|) le 1/2 is

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  20. Consider the following statement : S(1) : The value of int(0)^(2pi)c...

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