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Let: an=int0^(pi/2)(1-sint)^nsin2tdt T...

Let: `a_n=int_0^(pi/2)(1-sint)^nsin2tdt` Then find the value of `lim_(n->oo)na_n`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: int(-pi/2)^(2pi)sin^(-1)(sinx)dx

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  2. The value of int0^(pi/4)sin2xdx is

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  3. Let: an=int0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim(n->o...

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  4. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

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  5. Prove that int0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2)+.... .+ 1/...

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  6. Let f:[0,2]->R be a function which is continuous on [0,2] and is diff...

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  7. Evaluate: int0^1(1)/((1+x^2)sqrt(1-x^2))dx

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  8. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  9. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

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  10. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

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  11. Prove that 1 lt underset(0)overset(2)int((5-x)/(9-x^(2)))dx lt 6/5

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  12. If the difference between the roots of the equation x^2+""a x""+""1...

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  13. If m is the least value (global minimum) and M is the greatest value (...

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  14. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  15. Show that inta^b(|x|)/x dx=|b|-|a|dot

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  16. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

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  17. Let: f(x)=int0^x|2t-3|dtdot Then discuss continuity and differentiabil...

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  18. If inta^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is

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  19. L e tI1=int(pi/6)^(pi/3)(sinx)/x dx ,I2=int(pi/6)^(pi/3)sin(sinx)/(sin...

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  20. The value of int0^1e^(x^2-x)dx is (a)<1 (b) >1 (c) > e^(-1/4) ...

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