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Let In=int0^1(1-x^a)^n and if In/I(n+...

Let `I_n=int_0^1(1-x^a)^n` and if `I_n/I_(n+1)=1+lambda/alpha` then `lambda` equals (A) `n` (B) `n+1` (C) `1/n` (D) `1/(n+1)`

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BANSAL-INTEGRALS-All Questions
  1. Find the value of (lim)(n->oo)1/n+1/(n+1)+1/(n+2)+ddot+1/(4n)

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  2. Evaluate: int0^(pi//2)cos^2x\ dx

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  3. Let In=int0^1(1-x^a)^n and if In/I(n+1)=1+lambda/alpha then lambd...

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  4. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

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  5. int0^1(tan^(-1)x)/x dx is equals to int0^(pi/2)(sinx)/x dx (b)...

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  6. Evaluate : (lim)(x->0)(int0xtanx\ dx)/(xtanx)

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  7. Find the points of maxima of f(x)=int0^(x^2)(t^2-t)/(e^t+1)dtdot

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  8. Show that int0^1(dx)/(1+x^6)>pi/4

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  9. If int0^(10)f(x)dx=5, find the value of sum(k=1)^(10)int0^1f(k-1+x)dxd...

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  10. If y(x)=int(pi^2/16)^(x^2) (cosx cos sqrt(theta))/(1+sin^2 sqrt(theta)...

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  11. If In=int0^(pi//4)tan^n x dx , show that 1/(I2+I4),1/(I3+I5),1/(I4+...

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  12. Evaluate: lim(n->oo)[1/((n+1)^2\ )+1/((n+2)^2)+...+1/((2n)^2)]

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  13. Evaluate: inta^b e^x dx using limit of sum

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  14. Evaluate : (lim)(n->oo)sum(r=1)^n1/((n^2+r^2)^(1//2))

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  15. Evaluate the following definite integrals: int0^(pi//4)(sqrt(1-sin2...

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  16. Evaluate the following definite integrals: int0^(pi//2)xsinx sin2x d...

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  17. int0^(2pi)(dx)/(2+sin2x)

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  18. Evaluate the following definite integrals: int(1//e)^e|l\ n x|dx

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  19. Evaluate the following definite integral: int0^(pi//2)(sinx+cos x)dx

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  20. Evaluate the following definite integrals: int0^1(e^(-x))/(1+e^x)dx

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