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Prove that 4 lt= int1^3 sqrt(3+x^2) dx l...

Prove that `4 lt= int_1^3 sqrt(3+x^2) dx lt= 4sqrt(3)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

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  2. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  3. Prove that 4 lt= int1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

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  4. If I1=int0^(pi//2)(cos^2x)/(1+cos^2x)dx , I2=int0^(pi//2)(sin^2x)/(1+s...

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  5. Prove that int0^1sqrt((1+x)(1+x^3))\ dx cannot exceed sqrt((15)/8).

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  6. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  7. Evaluate: int0^1 1/(sqrt(1-x^2))sin^(-1)(2xsqrt(1-x^2))dxdot

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  8. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation x...

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  9. Evaluate: int(-pi//2)^(pi//2) sqrt(cosx-cos^3x) dx

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  10. If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function fo...

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  11. int(-1)^2|x^3-x|dxdot

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  12. If f(x) is integrable over [1,2], then int1^2f(x)dx is equal to (a) ...

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  13. Evaluate: int(-pi/2)^(pi)sin^(-1)(sinx)dx

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

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

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

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

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  18. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

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

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

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