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Evaluate: underset(nrarrinfty)lim (1/(n+...

Evaluate: `underset(nrarrinfty)lim (1/(n+1)+1/(n+2)+....+1/(2n))`

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. int0^3(absx+abs(x-1))dxis equal to

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  2. suppose for every integer n, intn^(n+1)f(x)dx=n^2then the value of int...

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  3. Evaluate: underset(nrarrinfty)lim (1/(n+1)+1/(n+2)+....+1/(2n))

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  4. The value of int 0^(2npi)[sin x+cosx]dx is equal to

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  5. the value ofint (pi/2)^(3pi/2)[2sinx]dx, is [.] greatest integer funct...

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  6. ifint0^1 f(x)dx=1,int0^1 xf(x)dx=a and int0^1 x^2f(x)dx=a^2 ,then int0...

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  7. if f(x)=-int0^xlog(cost)dt, then the value of f(x)-2f(pi/4+x/2)+2f(pi/...

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  8. if int0^(pi)(x/(1+sinx))^2dx=A, then int0^(pi)((2x^2).(cos^2(x/2)))/(1...

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  9. If intsin^4x/(cos^8x)dx= atan^7x+btan^5x+c then find the relation betw...

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  10. The value of x satisfying int0^(2[x+14]){x/2}dx=int0^({x})[x+14]dxis e...

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  11. if ngt1and I=int0^infty dx/((x+sqrt(1+x^2))^n then I equals

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  12. If [x] denotes the greatest integer lex and n inN then value of In=int...

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  13. if I=int0^1dx/((1+x)(2+x)sqrtx(1-x)then I equals

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  14. if int0^1 x(1-x)^(2007//2)dx then it equals

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  15. if I=int(-1)^2abs(xsinpix)dx then I equals

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  16. if I=int(alpha)^(beta)[loglogx+1/(logx)^2]dx then I equals

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  17. if I=int0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I eq...

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  18. if 0ltalphalt1 and I=int(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equal...

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  19. if I=int8^15 dx/((x-3)sqrt(x+1)) then I equals

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  20. underset(xrarr(pi//4))lim( int2^(sec^2x)(f(t)dt))/(x^2-(pi)^2/16 equal...

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