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Let alpha & beta be distinct positive ro...

Let `alpha` & `beta` be distinct positive roots of the equation `tanx = 2x`, then evaluate `int_(0)^(1)sin(alphax).sin(betax) dx`

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Evaluate int(0)^(pi)sqrt((cosx+cos2x+cos3x)^(2)+(sinx+sin2x+sin3x)^(...

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  2. Let alpha & beta be distinct positive roots of the equation tanx = 2x,...

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  3. Evaluate : lim(ararr(pi/2)^(-)) int(0)^(a)(cosx)ln(cosx)dx

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  4. Find the value of a(0 lt a lt 1) for which the following definite inte...

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  5. Find the Lim(nrarroo) ((""^(3n)C(n))/(""^(2n)C(n)))^(1/n) Where ""^(...

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  6. int0^oof(a/x+x/a)*(lnx)/x d x=lna*int(a/x+x/a)*(dx)/x

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  7. Evaluate Lim(n->oo)n^2 int(-1/n)^(1/n) (2006sinx+2007cosx) |x|dx

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  8. Find f(x) if it satisfies the relation f(x) = e^(x) + int(0)^(1) (x...

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  9. Evaluate the definite integral: int(-1/(sqrt(3)))^(1/(sqrt(3)))((x^4)/...

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  10. about to only mathematics

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  11. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

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  12. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

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  13. Let f(x) be a continuous function AA xepsilonR, except at x=0, such th...

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  14. Given that lim(nrarroo) sum(r=1)^(n) (log(e)(n^(2)+r^(2))-2log(e)n)/n ...

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  15. Given that lim(x to 0)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1,...

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  16. Sketch the graph of cos^(-1)(4x^3-3x) and find the area enclosed betwe...

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  17. Consider a square with vertices at (1, 1), (-1, 1), (-1, -1) and (1, -...

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  18. Let [x] denotes the greatest integer function. Draw a rough sketch of ...

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  19. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  20. Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + ...

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