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Prove that 1 lt int(0)^(2)((5-x)/(9-x^(2...

Prove that `1 lt int_(0)^(2)((5-x)/(9-x^(2)))dx lt 6/5`

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To prove that \( 1 < \int_{0}^{2} \frac{5-x}{9-x^2} \, dx < \frac{6}{5} \), we will evaluate the integral and find its bounds. ### Step 1: Define the function Let \[ f(x) = \frac{5-x}{9-x^2} \] ...
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Prove that 1 < int_0^2((5-x)/(9-x^2))dx < 6/5

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For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

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Prove that 0 lt int_0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Prove that 1 lt int(0)^(2)((5-x)/(9-x^(2)))dx lt 6/5

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  2. Evaluate int(0)^(pi)sqrt((cosx+cos2x+cos3x)^(2)+(sinx+sin2x+sin3x)^(...

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

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

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

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

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

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

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

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

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  11. about to only mathematics

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

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

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

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

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

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

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

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

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

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

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