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Find the value of int(-pi/3)^(pi/3)(pi...

Find the value of `int_(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx`

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  2. Evaluate: inta^b x^3dx

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  3. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

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  4. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

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  5. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

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  6. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

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  7. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

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  8. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

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  9. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

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  10. Prove that pi/6 lt int0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

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  11. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  12. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

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  13. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  14. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

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

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  16. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

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  17. If for a real number y ,[y] is the greatest integral function less, th...

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  18. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/(1+x^2)

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  19. int0^x{int0^uf(t)dx}\ du is equal to (a) int0^x(x-u)f(u)du (b) int0...

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  20. Compute the integrals: int(1/e)^e1/xsin(x-1/x)dx

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