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let g(x)=x^c e^(cx) and f(x)=int0^x t e...

let `g(x)=x^c e^(cx) and f(x)=int_0^x t e^(2t)(1+3t^2)^(1/2)dt`. if `L=lim_(x->oo) (f'(x))/(g'(x))` is non-zero finit number then :

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BANSAL-INTEGRALS-All Questions
  1. Evaluate: int0^(200pi)sqrt(1+cosx\ )"dx"

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  2. If y=a sin t, x=a cos t then find (dy)/(dx).

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  3. let g(x)=x^c e^(cx) and f(x)=int0^x t e^(2t)(1+3t^2)^(1/2)dt. if L=l...

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  4. Evaluate: inta^b cos x dx

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  5. Find the value of (lim)(n->oo)1/n+1/(n+1)+1/(n+2)+ddot+1/(4n)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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