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The number of positive continuous f(x) d...

The number of positive continuous `f(x)` defined in `[0,1]` for with `I_(1)=int_(0)^(1)f(x)dx=1,I_(2)=int_(0)^(1)xf(x)dx=a`,
`I_(3)=int_(0)^(1)x^(2)f(x)dx=a^(2)` is /are

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...

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  2. Show that int0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

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  3. The number of positive continuous f(x) defined in [0,1] for with I(1)=...

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  4. int 0^(pi/2) (sin^2x)/(sinx+cosx)dx

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  5. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is (a) s...

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  6. For theta in (0,pi/2), prove that int0^theta"log"(1+tanthetatanx)dx=th...

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  7. A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),...

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  8. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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  9. If P(x) is a polynomial of the least degree that has a maximum equal t...

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  10. Evaluate: int0^pixlogsinxdx

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  11. The value of the definite integral int0^(sqrt(1n(pi/2)))cose^(x^(2)...

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  12. Evaluate: int0^(π/2)cos2x+4sin2x cos2xdx

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  13. The value of int1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dx is...

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  14. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

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  15. If f(x) is monotonic differentiable function on [a , b] , then int...

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  16. L e tA=int0^oo(logx)/(1+x^3)dx Then find the value of int0^oo(xlogx)/(...

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  17. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

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  18. The value of lim(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi...

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  19. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

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  20. Match the statements/expression given in Column I with the values give...

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